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A Bibliography of works of Andrzej Mostowski
A Bibliography of works of Andrzej Mostowski (compiled by W. Marek) (*)
[1] Abzdhlbare Boolesche Kiirper und ihre Anwendung auf die allgemeine Metamathematik, Fund. Math. 29 (1937), pp. 34-53. {2] 0 niezaleznoici definicji skonczonosci w systemie logiki (On the independence of definitions of finiteness in a system of logic), Dodatek do Rocznika Polskiego Towarzystwa Matematycznego, vol. 11 (1938), pp.1-54. [3] Uber gewisse universelle Relationen; Ann. Soc. Pol. Math. 17 (1938), pp. 117-118. [4] Uber den Begriff einer endlichen Menge, Sprawozdania Towarzystwa Naukowego Warszawskiego (Cl. III) 31 (1938), pp. 13-20. [5] (with A. Lindenbaum) llber Unabhdngigkeit des Auswahlaxioms und einiger seiner Folgerungen, Sprawozdania Towarzystwa Naukowego Warszawskiego (Cl. III) 31 (1938), pp. 27-32. {6] (with A. Tarski) Boolesche Ringe mit geordneter Basis, Fund. Math. 32 (1939), pp. 69-86. [7] Uber die Undbhangigkeit des Wohlordnungssatzes von Ordnungsprinzip, Fund. Math. 32 (1939), pp. 201-252. [8] Bemerkungen zum Begriff der inhaltlichen Widerspruchsfreiheit, J. Symbolic Logic 4 (1939), pp. 113-114. [9] Remarques sur fa note de M. Sierpinski "Un theoreme sur les familles d'ensembles et ses applications", Fund. Math. 33 (1945), pp. 7-8. [10] AXiom of choice for finite sets, Fund. Math. 33 (1945), pp. 137-168. [11] 0 zdaniach nierozstrzygalnych w sformalizowanych systemach matematyki (On sentences undecidable in formalized systems of mathematics), Kwartalnik Filozoficzny 16 (1946), pp. 223-277. [12]* Zarys teorii Galois (An outline of Galois theory), supplement to Zasady algebry wyzszej (Foundations of higher algebra) by W. Sierpiriski, Monografie Matematyczne 11, Warszawa 1946, pp. 371-428. (*) Unfortunately, dealing with the bibliography of a scholar as prolific as A. Mostowski one cannot be sure that all the papers have been found and introduced. Still we hope that all the major papers have been included. We notice that the books are additionally marked with an asterisk.
XII
A BIBLIOGRAPHY OF WORKS OF A"IDRZEJ MOSTOWSKI
[13] On definable sets of positive integers, Fund. Math. 34 (1947), pp. 81-112. [14] On absolute properties of relations, J. Symbolic Logic 12 (1947), pp. 33-42. [15] On the principle of dependent choices, Fund. Math. 35 (1948), pp. 127-130. [16] Proofs of non-deducibility in intuitionistic functional calculus, J. Symbolic Logic 13 (1948), pp. 204-207. [17] On a set ofintegers not definable by means of one-quantifier predicates, Ann. Soc. Pol. Math. 21 (1948), pp. 114-119. [18] Un theoreme sur les nombres cos2rck/n, Colloq. Math. l/ (1948), pp. 195-196. [19]* Logika matematyczna, Kurs uniwersytecki (Mathematical logic, University course), Monografie Matematyczne 18, Warszawa-Wroclaw 1948, pp. VIII + 338. [20] An undecidable arithmetical statement, Fund. Math. 36 (1949), pp. 143-164. [21] Sur l'interpretation geometrique et topologique des notions logiques, Actes du Xveme Congres International de Philosophie (Amsterdam, 11-18 aout 1948), Amsterdam 1949, pp. 610-617. (22] (with A. Tarski) Arithmetical classes and types ofwell ordered systems, Bull. Amer. Math. Soc. 55 (1949), p. 65. [23] A general theorem concerning the decision problem, Bull. Amer. Math. Soc. 55 (1949), pp. 65-66. [24] (with A. Tarski) Undecidability in the arithmetic of integers and in the theory of rings, 1. Symbolic Logic 14 (1949), p. 76. [25] La vie et l'oeuvre de S. Dickstein, Prace Matematyczno-Fizyczne 47 (1949), pp. VII-XII. [26] Kilka refleksji na temat zadafi logicznych z "Matematyki" (Some remarks concerning problems on logic in "Maternatyka"), Matematyka 3 (3) (1950), pp. 6-11. [27] Some impredicative definitions In the axiomatic set-theory, Fund. Math. 37 (1951), pp. 111-124. Correction: ibid. 38 (1952), p. 238. [28] On the rules ofproof in the pure functional calculus of the first order, J. Symbolic Logic 16 (1951), pp. 107-111. [29] A classification of logical systems, Studia Philosophica 4 (1951), pp. 237-274. (30] (with K. Kuratowski) Sur un probleme de fa theorie des groupes et son rapport a la topologie, Colloq. Math. 2 (1951), pp. 212-215.
A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
XIII
[31] Groups connected with Boolean algebras (Partial solution of the Problem P92), Colloq. Math. 2 (1951), pp. 216-219. [32] On models of axiomatic systems, Fund. Math. 39 (1952), pp. 133-158. [33] On direct products of theories, J. Symbolic Logic 17 (1952),pp. 1-31. [34]* (with K. Kuratowski) Teoria mnogosci (Set theory), Monografie Maternatyczne 27, PWN-Polish Scientific Publishers, WarszawaWroclaw 1952, pp. IX + 311. (35]* Sentences undecidable In formalized arithmetic, An exposition of the theory of Kurt Giidel, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1952, pp. VIII + 117. (36] On a system of axioms which has no recursively enumerable arithmetic model, Fund. Math. 40 (1953), pp. 56-61. [37] A lemma concerning recursive functions and its applications, Bull. Acad, Pol. Sci. (el. III) 1 (1953), pp. 277-280 (Russian version: pp. 275-279). [38] 0 tzw. konstruktywnych prawach IV matematyce (On constructive principles in mathematics), Mysl Filozoficzna 1 (7) (1953), pp. 230-241. [39]* (with M. Stark) Algebra wytsza, cz. I (Higher algebra, part I), Biblioteka Matematyczna 1, PWN-Polish Scientific Publishers, Warszawa 1953, pp. VI + 308. [401 (with H. Rasiowa) 0 geometrycznej interpretacji wyraten logicznych (A geometrical interpretation of logical formulae), Studia Logica 1 (1953), pp. 254-273. [41J* (with R. M. Robinson and A. Tarski) Undecidability and essential undecidability in arithmetic, part II of Undecidable theories, by A. Tarski in collaboration with A. Mostowski and R. M. Robinson, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1953, pp. IX+98. [421* (with M: Stark) Algebra wytsza, cz. II (Higher algebra, part 11), Biblioteka Maternatyczna 3, PWN-Polish Scientific Publishers, Warszawa 1954, pp. VII + 173. [43]* (with M. Stark) Algebra wytsza, cz. III (Higher algebra, part III), Biblioteka Matematyczna 4, PWN-Polish Scientific Publishers, 1st ed., Warszawa 1954, 3rd ed., Warszawa 1967, pp. VII+268. [44] Podstawy matematyki na VIII Zjeidzie Matematykow Polskich (Foundations of mathematics at the VIIlth Congress of Polish Mathematicians), Mysl FiIozoficzna 2 (12) (1954), pp. 328-330.
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A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
[45} Development and applications of the "projective" classification of sets ofintegers, Proceedings of the International Congress of Mathematicians, 1954, vol. Ill, E. P. Noordhoff N. V., Groningen and North-Holland Publishing Co., Amsterdam 1956, pp. 280-288. [46] (with A. Grzegorczyk, S. Jaskowski, J. Los, S. Mazur, H. Rasiowa and R. Sikorski) The present state of investigations offoundations of mathematics, Rozprawy Matematyczne (Dissertationes Mathematicae) 9 (1955), pp. 1-48; German translation in: Die Hauptreferate des 8. Polnischen Mathematikerkongresses vom 6. bis 12. September 1950 in Warschau, Berlin 1954, pp. 11-44; Russian translation: Coepeuenuoe
cocmonuue uccneooeauuii no OCHoeaHURM uamesamusu,
Ycnexa MaT. Hayx 9 (1954), pp. 3-38. [47] A formula with no recursively enumerable model, Fund. Math. 42 (1955), pp. 125-140. [48] Examples of sets definable by means of two and three quantifiers Fund. Math. 42 (1955), pp. 259-270. [49} Contributions to the theory of-definable sets and functions, Fund. Math. 42 (1955), pp. 271-275. [50} (withJ. Los and H. Rasiowa) A proofofHerbrand's theorem, J. Math. Pures et Appl. 34 (1955), pp. 19-24. [51} Eine Verallgemeinerung eines Satzes von M. Deuring, Acta Sci. Math. Szeged 16 (1955), pp. 197-203. [52) Wspolczesny stan badafi nad podstawami matematyki (The present state of investigations of foundations of mathematics), Prace Matematyczne 1 (1955), pp. 13-55. [53} Wyznaczanie stopni niektorych liczb algebraicznych (Evaluating degrees of some algebraic numbers), Prace Matematyczne 1 (1955), pp. 239-252. [54} (with A. Ehrenfeucht) Models of axiomatic theories admitting automorphisms, Fund. Math. 43 (1956), pp. 50-68. [55) Concerning a problem of H. Scholz, Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 2 (1956), pp. 210-214. [56] On models of axiomatic set theory, Bull. Acad. Pol. Sci. (Cl. III) 4 (1956), pp. 663-667. [57} Logika matematyczna na Miedzynarodowym Zjeidzie Matematykow w Amsterdamie (Mathematical logic at the International Congress of Mathematicians in Amsterdam), Studia Logica 4 (1956), pp. 245-253.
A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
xv
[58] L'oeuvre scientifique de Jan Lukasiewicz dans Ie domaine de la logique mathematique, Fund. Math. 44 (1957), pp. 1-11.
[591 On a generalization of quantifiers, Fund. Math. 44 (1957), pp. 12-36. [601 On computable sequences, Fund. Math. 44 (1957), pp. 37-51. [61] On recursive models of formalized arithmetic, Bull. Acad. Pol. Sci. (CI. III) 5 (1957), pp. 705-710. [62] (with A. Grzegorczyk and Cz. Ryll-Nardzewski) The classical and the oi-complete arithmetic, J. Symbolic Logic 23 (1958), pp. 188-206. [63] On a problem of W. Kinna and K. Wagner, Colloq. Math. 6 (1958), pp. 207-208. [64] (with Cz, Ryll-Nardzewski) Representability of sets in models of axiomatic theories, J. Symbolic' Logic 23 (1958), p. 458. [65] Quelques observations sur l'usage des methodes non-finitistes dans la metamathematique, Le raisonnement en mathematiques et en sciences experimentales, Editions du Centre National de la Recherche Scientifique, Paris 1958, pp. 19-32. [66] A semantical characterization of invariant and absolute formulas, Abstracts of short communications and scientific programme of the International Congress of Mathematicians, Edinburgh 1958,p. 9. [67]* (with M. Stark) Elementy algebry wyzszej (Introduction to higher algebra), Biblioteka Matematyczna 16, PWN-Polish Scientific Publishers, l.st ed., Warszawa 1958, 8th ed., Warszawa 1975, pp. 1-400. [68]* (with M. Stark) Algebra liniowa (Linear algebra), Biblioteka Matematyczna 19, PWN-Polish Scientific Publishers, Ist ed., Warszawa 1958, 5th ed., Warszawa 1976, pp. 1-188. [69] On various degrees of constructivism, Constructivity in mathematics, Proceedings of the Colloquium held in Amsterdam, 1957, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1959, pp. 178-194. [70] A class of models of second-order arithmetic, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 7 (1969), pp. 401-404. (71) 3aJ4e'laHUR K ooxasomeascmeau cytqecmeoeauun cmauoapmuux MOOeJleU, TpY,lJ;bI Tpersero Bcecoioaaoro Mareaarnnecxoro Oseana, TOM 4, H3,lJ;aTe.YlbCTBO AH CCCP, Mocxna 1959, pp. 232-236. [72] Formal system of analysis based on an infinitistic rule of proof, Infinitistic Methods, Proceedings of Symposium on Foundations of Mathematics, PWN-Polish Scientific Publishers, Warszawa and Pergamon Press, New York-Oxford-London-Paris 1961, pp. 141-166.
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A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
{73] Completeness theorems for some many valuedpredicate calculi, J. Symbolic Logic 25 (1960), pp. 94-95. [74] A generalization of the incompleteness theorem, Fund. Math. 49 (1961), pp. 205-232. [75] An example of a non-axiomatizable many valued logic, Zeitschrift fllr Mathematische Logik und Grundlagen der Mathematik 7 (1961), pp. 72-76. {76] Concerning the problem ofaxiomatizability of the field of real numbers in the weak second order logic, Essays on the Foundations of Mathematics, ed. Y. Bar-Hillel et al., Magnes Press, Jerusalem 1961, pp. 269-286. [77] (with A. Grzegorczyk and Cz, Ryll-Nardzewski) Definability of sets in models of axiomatic theories, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys, 9 (1961), pp. 163-167. [78] (with A. Ehrenfeucht) A compact space of models of first order theories, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys, 9 (1961), pp. 369-373. [79] (with J. Los and H. Rasiowa) Addition au travail "A proof of Herbrand's theorem", J. Math. Pures et Appl. 40 (1961), pp. 129-134. [80] Axiomatizability of some many valued predicate calculi,' Fund. Math. 50 (1961-1962), pp. 165-190. [81] Representability of sets informal systems, Recursive function theory, Proceedings of Symposia in Pure Mathematics, vol. V, American Mathematical Society, Providence, Rhode Island, 1962, pp. 29--48. [82] A problem in the theory of models, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. W (1962), pp. 121-126. [83] On invariant, dual invariant, and absolute formulas, Rozprawy Matematyczne (Dissertationes Mathematicae) XXIX (1962), pp. 1-38. 184] L'espace des modeles d'une theorie formalisee et quelques-unes des applications, Annales de la Faculte des Sciences de L'Universite Clermont 7 (1962), pp. 107-116. [85] The Hilbert epsilon function in many-valued logics, Acta Phil. Fennica 16 (1963), pp. 169-188. [86}* (with M. Stark) Introduction to higher algebra, PWN-Polish Scientific Publishers, Warszawa and Pergamon Press, Oxford-LondonNew York-Paris, 1963, pp. 474. [87] Widerspruchsfreiheit und Unabhiingigkeit der Kontinuumhypothese, Elemente der Mathematik 19 (1964), pp. 121-125.
A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
XVII
[88] On models of Zermelo-Fraenkel set theory satisfying the axiom of constructibility, Acta Phil. Fennica 18 (1965), pp. 135-144. [89]* Thirty years of foundational studies, Lectures on the development of mathematical logic and the study of the foundations of mathematics in 1930-1964, Acta Phil. Fennica XVII (1965), pp. 1-180. [90]* (with K. Kuratowski) Teoriamnogosci (Set theory), 2nd ed. revised, Monografie Matematyczne 27, PWN-Polish Scientific Publishers, Warszawa 1966, pp. 1-375. [91]* Modeles transitifs de la theorie des ensembles de Zermelo-Fraenkel, Les Press de l'Universite de Montreal 1967, pp. 1-170. [92] Recent results in set theory, Problems in the philosophy of mathematics, ed. J. Lakatos, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1967, pp. 82-96 and 105-108. [93] 0 niektorych nowych wynikach matematycznych dotyczqcych teorli mnogosci (On some new mathematical results concerning set theory), Studia Logica 20 (1967), pp. 99-116. [94] Tarski Alfred, The Encyclopedia of Philosophy, vol. 8, ed. Paul Edwards, MacMillan and Free Press, New York-1967, pp. 77-81. [95]* (with K. Kuratowski) Set theory, Studies in Logic and the Foundations of Mathematics, PWN-Polish Scientific Publishers, Warszawa and North-Holland Publishing Co., Amsterdam-New YorkOxford, 1967, pp. 1-417. 196] Craig's interpolation theorem in some extended systems of logic, Logic Methodology and Philosophy of Science III, Proceedings of the Third International Congress for Logic, Methodology and Philosophy of Science, ed. B. van Rootselaar and J. F. Staal, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1968, pp. 87-103. {97] Models of set theory, Lectures delivered in Varenna, September 1968, C.LM.E., Italy 1968, pp. 67-179. [98] Niesprzecznoie i niezaleznosc hipotezy continuum (Consistency and independence of continuum hypothesis), Wiadomosci Matematyczne 10 (1968), pp. 175-182. [99] (with Y. Suzuki) On co-models which are not f3-models, Fund. Math. 65 (1969), pp. 83-93. [100]* Constructible sets with applications, Studies in Logic and the Foundations of Mathematics, PWN-Polish Scientific Publishers, Warszawa and North-Holland Publishing Co., Amsterdam, 1969, pp. 1-269.
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A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
[ltH]* (with K. Kuratowski) Teopun MHO:HCecm8, MHP, Mocxna 1970, pp. 1-416. [102] Models of second order· arithmetic with definable Skolem functions, Fund. Math. 75 (1972), pp. 223-234. Correction: ibid. 84 (1974), p. 173. [103] A transfinite sequence of to-models, J. Symbolic Logic 37 (1972), pp. 96-102. [104] Sets, Scientific thought, Some underlying concepts, methods and procedures, Mouton/Unesco, Paris-Hague 1972, pp. 1-34. [105] Matematyka a logika. Refleksje przy lekturze ksiqzki A. Grzegorczyka "Zarys arytmetyki tearetycznej" wraz z proba recenzji (Mathematics vs. logic. Impressions of the study of "Outline of theoretical arithmetic" by A.:Grzegorczyk with an attempt of review), Wiadomosci Matematyczne 15 (1972), pp. 79-89. [106] Partial ordering of the family of co-models, Logic, Methodology and Philosophy of Science IV, Studies in Logic and the Foundations of Mathematics, PWN-Polish Scientific Publishers, Warszawa and North-Holland, Amsterdam-London, 1973, pp. 13-28. [107] A contribution to teratology, Hsfipaaasre BOnpOCbI anreopsr H JIorHKH, Hayxa, hOBOCH6HpCK, 1973, pp. 184-196. [108]* Koncmpyxmueuue MHO:HCecmea U ux npUJlO:HCeHUR, MHP, MOCKBa 1973, pp. 1-256. [109] Some problems in the axiomatic theory of classes, Bolletino U.M.I. 4 (9), SuppI. Fasc. 2 (1974), pp. 161-170. [110] Refieksje na temat pewnego wyk/adu z historii matematyki (Impressions on certain course of the history of mathematics), 0 nauczaniu matematyki, Ossolineum, Wroclaw-Warszawa 1974, pp. 231-243. [111] Observations concerning elementary extensions of w -models I, Proceedings of the Tarski Symposium, ed. L. Henkin et al., Proceedings of Symposia in Pure Mathematics 25, Americal Mathematical Society, Providence, Rhode Island, 1975, pp. 349-355. [112] An exposition offorcing, Algebra and logic, Lecture Notes in Mathematics 450, Springer-Verlag, Berlin-Heidelberg-New York, 1975, pp. 22()"'282. [113] (with W. Marek) On extendability of models of ZF set theory to the models of Kelley-Morse theory of classes, Logic Conference, Kiel 1974, Lecture Notes in Mathematics 499, Springer-Verlag, BerlinHeidelberg-New York, 1975, pp. 460-542.
A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
XIX
[114] Szkola a uniwersytet (School vs, university), Wiadomosci Matematyczne 19 (1975), pp. 51-60. [115] Travaux de W. Sierpinski sur la theorie des ensembles et ses applications. La theorie generale des ensembles, introduction to: Waclaw Sierpinski, Oeuvres choisies, Tome II, PWN-PoJish Scientific Publishers, Warszawa 1975, pp. 9-13. [116] Remarks on models of Morse's set theory, Memorial Tribute to A. Mostowski, Lecture Notes in Mathematics 537, Springer-Verlag, Berlin-Heidelberg-New York, 1976, pp. 13-21. [117] A remark on models of the Giidel-Bemays axioms for set theory, Sets and classes, On the work by P. Bernays, ed. G. H. Muller. Studies in Logic and the Foundations of Mathematics, NorthHolland Publishing Co., Amsterdam-New York-Oxford, 1976, pp. 325-340. [118]* (with K. Kuratowski) Set theory, with an introduction to descriptive set theory, PWN-Polish Scientific Publishers, Warszawa and North-Holland Publishing Co., Amsterdam-New York-Oxford, 1976, pp. XIV +514. [119] (with J. Donner and A. Tarski) Decidability of the theory of wellorderings (to appear in Wroclaw Conference Proceedings).
[1] Abzdhlbare Boolesche Kiirper und ihre Anwendung auf die allgemeine Metamathematik, Fund. Math. 29 (1937), pp. 34-53. {2] 0 niezaleznoici definicji skonczonosci w systemie logiki (On the independence of definitions of finiteness in a system of logic), Dodatek do Rocznika Polskiego Towarzystwa Matematycznego, vol. 11 (1938), pp.1-54. [3] Uber gewisse universelle Relationen; Ann. Soc. Pol. Math. 17 (1938), pp. 117-118. [4] Uber den Begriff einer endlichen Menge, Sprawozdania Towarzystwa Naukowego Warszawskiego (Cl. III) 31 (1938), pp. 13-20. [5] (with A. Lindenbaum) llber Unabhdngigkeit des Auswahlaxioms und einiger seiner Folgerungen, Sprawozdania Towarzystwa Naukowego Warszawskiego (Cl. III) 31 (1938), pp. 27-32. {6] (with A. Tarski) Boolesche Ringe mit geordneter Basis, Fund. Math. 32 (1939), pp. 69-86. [7] Uber die Undbhangigkeit des Wohlordnungssatzes von Ordnungsprinzip, Fund. Math. 32 (1939), pp. 201-252. [8] Bemerkungen zum Begriff der inhaltlichen Widerspruchsfreiheit, J. Symbolic Logic 4 (1939), pp. 113-114. [9] Remarques sur fa note de M. Sierpinski "Un theoreme sur les familles d'ensembles et ses applications", Fund. Math. 33 (1945), pp. 7-8. [10] AXiom of choice for finite sets, Fund. Math. 33 (1945), pp. 137-168. [11] 0 zdaniach nierozstrzygalnych w sformalizowanych systemach matematyki (On sentences undecidable in formalized systems of mathematics), Kwartalnik Filozoficzny 16 (1946), pp. 223-277. [12]* Zarys teorii Galois (An outline of Galois theory), supplement to Zasady algebry wyzszej (Foundations of higher algebra) by W. Sierpiriski, Monografie Matematyczne 11, Warszawa 1946, pp. 371-428. (*) Unfortunately, dealing with the bibliography of a scholar as prolific as A. Mostowski one cannot be sure that all the papers have been found and introduced. Still we hope that all the major papers have been included. We notice that the books are additionally marked with an asterisk.
XII
A BIBLIOGRAPHY OF WORKS OF A"IDRZEJ MOSTOWSKI
[13] On definable sets of positive integers, Fund. Math. 34 (1947), pp. 81-112. [14] On absolute properties of relations, J. Symbolic Logic 12 (1947), pp. 33-42. [15] On the principle of dependent choices, Fund. Math. 35 (1948), pp. 127-130. [16] Proofs of non-deducibility in intuitionistic functional calculus, J. Symbolic Logic 13 (1948), pp. 204-207. [17] On a set ofintegers not definable by means of one-quantifier predicates, Ann. Soc. Pol. Math. 21 (1948), pp. 114-119. [18] Un theoreme sur les nombres cos2rck/n, Colloq. Math. l/ (1948), pp. 195-196. [19]* Logika matematyczna, Kurs uniwersytecki (Mathematical logic, University course), Monografie Matematyczne 18, Warszawa-Wroclaw 1948, pp. VIII + 338. [20] An undecidable arithmetical statement, Fund. Math. 36 (1949), pp. 143-164. [21] Sur l'interpretation geometrique et topologique des notions logiques, Actes du Xveme Congres International de Philosophie (Amsterdam, 11-18 aout 1948), Amsterdam 1949, pp. 610-617. (22] (with A. Tarski) Arithmetical classes and types ofwell ordered systems, Bull. Amer. Math. Soc. 55 (1949), p. 65. [23] A general theorem concerning the decision problem, Bull. Amer. Math. Soc. 55 (1949), pp. 65-66. [24] (with A. Tarski) Undecidability in the arithmetic of integers and in the theory of rings, 1. Symbolic Logic 14 (1949), p. 76. [25] La vie et l'oeuvre de S. Dickstein, Prace Matematyczno-Fizyczne 47 (1949), pp. VII-XII. [26] Kilka refleksji na temat zadafi logicznych z "Matematyki" (Some remarks concerning problems on logic in "Maternatyka"), Matematyka 3 (3) (1950), pp. 6-11. [27] Some impredicative definitions In the axiomatic set-theory, Fund. Math. 37 (1951), pp. 111-124. Correction: ibid. 38 (1952), p. 238. [28] On the rules ofproof in the pure functional calculus of the first order, J. Symbolic Logic 16 (1951), pp. 107-111. [29] A classification of logical systems, Studia Philosophica 4 (1951), pp. 237-274. (30] (with K. Kuratowski) Sur un probleme de fa theorie des groupes et son rapport a la topologie, Colloq. Math. 2 (1951), pp. 212-215.
A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
XIII
[31] Groups connected with Boolean algebras (Partial solution of the Problem P92), Colloq. Math. 2 (1951), pp. 216-219. [32] On models of axiomatic systems, Fund. Math. 39 (1952), pp. 133-158. [33] On direct products of theories, J. Symbolic Logic 17 (1952),pp. 1-31. [34]* (with K. Kuratowski) Teoria mnogosci (Set theory), Monografie Maternatyczne 27, PWN-Polish Scientific Publishers, WarszawaWroclaw 1952, pp. IX + 311. (35]* Sentences undecidable In formalized arithmetic, An exposition of the theory of Kurt Giidel, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1952, pp. VIII + 117. (36] On a system of axioms which has no recursively enumerable arithmetic model, Fund. Math. 40 (1953), pp. 56-61. [37] A lemma concerning recursive functions and its applications, Bull. Acad, Pol. Sci. (el. III) 1 (1953), pp. 277-280 (Russian version: pp. 275-279). [38] 0 tzw. konstruktywnych prawach IV matematyce (On constructive principles in mathematics), Mysl Filozoficzna 1 (7) (1953), pp. 230-241. [39]* (with M. Stark) Algebra wytsza, cz. I (Higher algebra, part I), Biblioteka Matematyczna 1, PWN-Polish Scientific Publishers, Warszawa 1953, pp. VI + 308. [401 (with H. Rasiowa) 0 geometrycznej interpretacji wyraten logicznych (A geometrical interpretation of logical formulae), Studia Logica 1 (1953), pp. 254-273. [41J* (with R. M. Robinson and A. Tarski) Undecidability and essential undecidability in arithmetic, part II of Undecidable theories, by A. Tarski in collaboration with A. Mostowski and R. M. Robinson, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1953, pp. IX+98. [421* (with M: Stark) Algebra wytsza, cz. II (Higher algebra, part 11), Biblioteka Maternatyczna 3, PWN-Polish Scientific Publishers, Warszawa 1954, pp. VII + 173. [43]* (with M. Stark) Algebra wytsza, cz. III (Higher algebra, part III), Biblioteka Matematyczna 4, PWN-Polish Scientific Publishers, 1st ed., Warszawa 1954, 3rd ed., Warszawa 1967, pp. VII+268. [44] Podstawy matematyki na VIII Zjeidzie Matematykow Polskich (Foundations of mathematics at the VIIlth Congress of Polish Mathematicians), Mysl FiIozoficzna 2 (12) (1954), pp. 328-330.
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A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
[45} Development and applications of the "projective" classification of sets ofintegers, Proceedings of the International Congress of Mathematicians, 1954, vol. Ill, E. P. Noordhoff N. V., Groningen and North-Holland Publishing Co., Amsterdam 1956, pp. 280-288. [46] (with A. Grzegorczyk, S. Jaskowski, J. Los, S. Mazur, H. Rasiowa and R. Sikorski) The present state of investigations offoundations of mathematics, Rozprawy Matematyczne (Dissertationes Mathematicae) 9 (1955), pp. 1-48; German translation in: Die Hauptreferate des 8. Polnischen Mathematikerkongresses vom 6. bis 12. September 1950 in Warschau, Berlin 1954, pp. 11-44; Russian translation: Coepeuenuoe
cocmonuue uccneooeauuii no OCHoeaHURM uamesamusu,
Ycnexa MaT. Hayx 9 (1954), pp. 3-38. [47] A formula with no recursively enumerable model, Fund. Math. 42 (1955), pp. 125-140. [48] Examples of sets definable by means of two and three quantifiers Fund. Math. 42 (1955), pp. 259-270. [49} Contributions to the theory of-definable sets and functions, Fund. Math. 42 (1955), pp. 271-275. [50} (withJ. Los and H. Rasiowa) A proofofHerbrand's theorem, J. Math. Pures et Appl. 34 (1955), pp. 19-24. [51} Eine Verallgemeinerung eines Satzes von M. Deuring, Acta Sci. Math. Szeged 16 (1955), pp. 197-203. [52) Wspolczesny stan badafi nad podstawami matematyki (The present state of investigations of foundations of mathematics), Prace Matematyczne 1 (1955), pp. 13-55. [53} Wyznaczanie stopni niektorych liczb algebraicznych (Evaluating degrees of some algebraic numbers), Prace Matematyczne 1 (1955), pp. 239-252. [54} (with A. Ehrenfeucht) Models of axiomatic theories admitting automorphisms, Fund. Math. 43 (1956), pp. 50-68. [55) Concerning a problem of H. Scholz, Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 2 (1956), pp. 210-214. [56] On models of axiomatic set theory, Bull. Acad. Pol. Sci. (Cl. III) 4 (1956), pp. 663-667. [57} Logika matematyczna na Miedzynarodowym Zjeidzie Matematykow w Amsterdamie (Mathematical logic at the International Congress of Mathematicians in Amsterdam), Studia Logica 4 (1956), pp. 245-253.
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[58] L'oeuvre scientifique de Jan Lukasiewicz dans Ie domaine de la logique mathematique, Fund. Math. 44 (1957), pp. 1-11.
[591 On a generalization of quantifiers, Fund. Math. 44 (1957), pp. 12-36. [601 On computable sequences, Fund. Math. 44 (1957), pp. 37-51. [61] On recursive models of formalized arithmetic, Bull. Acad. Pol. Sci. (CI. III) 5 (1957), pp. 705-710. [62] (with A. Grzegorczyk and Cz. Ryll-Nardzewski) The classical and the oi-complete arithmetic, J. Symbolic Logic 23 (1958), pp. 188-206. [63] On a problem of W. Kinna and K. Wagner, Colloq. Math. 6 (1958), pp. 207-208. [64] (with Cz, Ryll-Nardzewski) Representability of sets in models of axiomatic theories, J. Symbolic' Logic 23 (1958), p. 458. [65] Quelques observations sur l'usage des methodes non-finitistes dans la metamathematique, Le raisonnement en mathematiques et en sciences experimentales, Editions du Centre National de la Recherche Scientifique, Paris 1958, pp. 19-32. [66] A semantical characterization of invariant and absolute formulas, Abstracts of short communications and scientific programme of the International Congress of Mathematicians, Edinburgh 1958,p. 9. [67]* (with M. Stark) Elementy algebry wyzszej (Introduction to higher algebra), Biblioteka Matematyczna 16, PWN-Polish Scientific Publishers, l.st ed., Warszawa 1958, 8th ed., Warszawa 1975, pp. 1-400. [68]* (with M. Stark) Algebra liniowa (Linear algebra), Biblioteka Matematyczna 19, PWN-Polish Scientific Publishers, Ist ed., Warszawa 1958, 5th ed., Warszawa 1976, pp. 1-188. [69] On various degrees of constructivism, Constructivity in mathematics, Proceedings of the Colloquium held in Amsterdam, 1957, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1959, pp. 178-194. [70] A class of models of second-order arithmetic, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 7 (1969), pp. 401-404. (71) 3aJ4e'laHUR K ooxasomeascmeau cytqecmeoeauun cmauoapmuux MOOeJleU, TpY,lJ;bI Tpersero Bcecoioaaoro Mareaarnnecxoro Oseana, TOM 4, H3,lJ;aTe.YlbCTBO AH CCCP, Mocxna 1959, pp. 232-236. [72] Formal system of analysis based on an infinitistic rule of proof, Infinitistic Methods, Proceedings of Symposium on Foundations of Mathematics, PWN-Polish Scientific Publishers, Warszawa and Pergamon Press, New York-Oxford-London-Paris 1961, pp. 141-166.
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A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
{73] Completeness theorems for some many valuedpredicate calculi, J. Symbolic Logic 25 (1960), pp. 94-95. [74] A generalization of the incompleteness theorem, Fund. Math. 49 (1961), pp. 205-232. [75] An example of a non-axiomatizable many valued logic, Zeitschrift fllr Mathematische Logik und Grundlagen der Mathematik 7 (1961), pp. 72-76. {76] Concerning the problem ofaxiomatizability of the field of real numbers in the weak second order logic, Essays on the Foundations of Mathematics, ed. Y. Bar-Hillel et al., Magnes Press, Jerusalem 1961, pp. 269-286. [77] (with A. Grzegorczyk and Cz, Ryll-Nardzewski) Definability of sets in models of axiomatic theories, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys, 9 (1961), pp. 163-167. [78] (with A. Ehrenfeucht) A compact space of models of first order theories, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys, 9 (1961), pp. 369-373. [79] (with J. Los and H. Rasiowa) Addition au travail "A proof of Herbrand's theorem", J. Math. Pures et Appl. 40 (1961), pp. 129-134. [80] Axiomatizability of some many valued predicate calculi,' Fund. Math. 50 (1961-1962), pp. 165-190. [81] Representability of sets informal systems, Recursive function theory, Proceedings of Symposia in Pure Mathematics, vol. V, American Mathematical Society, Providence, Rhode Island, 1962, pp. 29--48. [82] A problem in the theory of models, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. W (1962), pp. 121-126. [83] On invariant, dual invariant, and absolute formulas, Rozprawy Matematyczne (Dissertationes Mathematicae) XXIX (1962), pp. 1-38. 184] L'espace des modeles d'une theorie formalisee et quelques-unes des applications, Annales de la Faculte des Sciences de L'Universite Clermont 7 (1962), pp. 107-116. [85] The Hilbert epsilon function in many-valued logics, Acta Phil. Fennica 16 (1963), pp. 169-188. [86}* (with M. Stark) Introduction to higher algebra, PWN-Polish Scientific Publishers, Warszawa and Pergamon Press, Oxford-LondonNew York-Paris, 1963, pp. 474. [87] Widerspruchsfreiheit und Unabhiingigkeit der Kontinuumhypothese, Elemente der Mathematik 19 (1964), pp. 121-125.
A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
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[88] On models of Zermelo-Fraenkel set theory satisfying the axiom of constructibility, Acta Phil. Fennica 18 (1965), pp. 135-144. [89]* Thirty years of foundational studies, Lectures on the development of mathematical logic and the study of the foundations of mathematics in 1930-1964, Acta Phil. Fennica XVII (1965), pp. 1-180. [90]* (with K. Kuratowski) Teoriamnogosci (Set theory), 2nd ed. revised, Monografie Matematyczne 27, PWN-Polish Scientific Publishers, Warszawa 1966, pp. 1-375. [91]* Modeles transitifs de la theorie des ensembles de Zermelo-Fraenkel, Les Press de l'Universite de Montreal 1967, pp. 1-170. [92] Recent results in set theory, Problems in the philosophy of mathematics, ed. J. Lakatos, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1967, pp. 82-96 and 105-108. [93] 0 niektorych nowych wynikach matematycznych dotyczqcych teorli mnogosci (On some new mathematical results concerning set theory), Studia Logica 20 (1967), pp. 99-116. [94] Tarski Alfred, The Encyclopedia of Philosophy, vol. 8, ed. Paul Edwards, MacMillan and Free Press, New York-1967, pp. 77-81. [95]* (with K. Kuratowski) Set theory, Studies in Logic and the Foundations of Mathematics, PWN-Polish Scientific Publishers, Warszawa and North-Holland Publishing Co., Amsterdam-New YorkOxford, 1967, pp. 1-417. 196] Craig's interpolation theorem in some extended systems of logic, Logic Methodology and Philosophy of Science III, Proceedings of the Third International Congress for Logic, Methodology and Philosophy of Science, ed. B. van Rootselaar and J. F. Staal, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam 1968, pp. 87-103. {97] Models of set theory, Lectures delivered in Varenna, September 1968, C.LM.E., Italy 1968, pp. 67-179. [98] Niesprzecznoie i niezaleznosc hipotezy continuum (Consistency and independence of continuum hypothesis), Wiadomosci Matematyczne 10 (1968), pp. 175-182. [99] (with Y. Suzuki) On co-models which are not f3-models, Fund. Math. 65 (1969), pp. 83-93. [100]* Constructible sets with applications, Studies in Logic and the Foundations of Mathematics, PWN-Polish Scientific Publishers, Warszawa and North-Holland Publishing Co., Amsterdam, 1969, pp. 1-269.
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A BIBLIOGRAPHY OF WORKS OF ANDRZEJ MOSTOWSKI
[ltH]* (with K. Kuratowski) Teopun MHO:HCecm8, MHP, Mocxna 1970, pp. 1-416. [102] Models of second order· arithmetic with definable Skolem functions, Fund. Math. 75 (1972), pp. 223-234. Correction: ibid. 84 (1974), p. 173. [103] A transfinite sequence of to-models, J. Symbolic Logic 37 (1972), pp. 96-102. [104] Sets, Scientific thought, Some underlying concepts, methods and procedures, Mouton/Unesco, Paris-Hague 1972, pp. 1-34. [105] Matematyka a logika. Refleksje przy lekturze ksiqzki A. Grzegorczyka "Zarys arytmetyki tearetycznej" wraz z proba recenzji (Mathematics vs. logic. Impressions of the study of "Outline of theoretical arithmetic" by A.:Grzegorczyk with an attempt of review), Wiadomosci Matematyczne 15 (1972), pp. 79-89. [106] Partial ordering of the family of co-models, Logic, Methodology and Philosophy of Science IV, Studies in Logic and the Foundations of Mathematics, PWN-Polish Scientific Publishers, Warszawa and North-Holland, Amsterdam-London, 1973, pp. 13-28. [107] A contribution to teratology, Hsfipaaasre BOnpOCbI anreopsr H JIorHKH, Hayxa, hOBOCH6HpCK, 1973, pp. 184-196. [108]* Koncmpyxmueuue MHO:HCecmea U ux npUJlO:HCeHUR, MHP, MOCKBa 1973, pp. 1-256. [109] Some problems in the axiomatic theory of classes, Bolletino U.M.I. 4 (9), SuppI. Fasc. 2 (1974), pp. 161-170. [110] Refieksje na temat pewnego wyk/adu z historii matematyki (Impressions on certain course of the history of mathematics), 0 nauczaniu matematyki, Ossolineum, Wroclaw-Warszawa 1974, pp. 231-243. [111] Observations concerning elementary extensions of w -models I, Proceedings of the Tarski Symposium, ed. L. Henkin et al., Proceedings of Symposia in Pure Mathematics 25, Americal Mathematical Society, Providence, Rhode Island, 1975, pp. 349-355. [112] An exposition offorcing, Algebra and logic, Lecture Notes in Mathematics 450, Springer-Verlag, Berlin-Heidelberg-New York, 1975, pp. 22()"'282. [113] (with W. Marek) On extendability of models of ZF set theory to the models of Kelley-Morse theory of classes, Logic Conference, Kiel 1974, Lecture Notes in Mathematics 499, Springer-Verlag, BerlinHeidelberg-New York, 1975, pp. 460-542.
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[114] Szkola a uniwersytet (School vs, university), Wiadomosci Matematyczne 19 (1975), pp. 51-60. [115] Travaux de W. Sierpinski sur la theorie des ensembles et ses applications. La theorie generale des ensembles, introduction to: Waclaw Sierpinski, Oeuvres choisies, Tome II, PWN-PoJish Scientific Publishers, Warszawa 1975, pp. 9-13. [116] Remarks on models of Morse's set theory, Memorial Tribute to A. Mostowski, Lecture Notes in Mathematics 537, Springer-Verlag, Berlin-Heidelberg-New York, 1976, pp. 13-21. [117] A remark on models of the Giidel-Bemays axioms for set theory, Sets and classes, On the work by P. Bernays, ed. G. H. Muller. Studies in Logic and the Foundations of Mathematics, NorthHolland Publishing Co., Amsterdam-New York-Oxford, 1976, pp. 325-340. [118]* (with K. Kuratowski) Set theory, with an introduction to descriptive set theory, PWN-Polish Scientific Publishers, Warszawa and North-Holland Publishing Co., Amsterdam-New York-Oxford, 1976, pp. XIV +514. [119] (with J. Donner and A. Tarski) Decidability of the theory of wellorderings (to appear in Wroclaw Conference Proceedings).