Index of Definitions and Abbreviations*

INDEX OF DEFINITIONS AND ABBREVIATIONS*

wl (algebraic closure) ad missib1e

acl(A)

111,Definition 6.1(4), p. 130

AD el (after last) algebraic

(1) Fa-admissible (2) F-*admissible (3) F-**admissible

A D ( A , x , p, K ) al(4 (1) algebraic formula [type], d algebraic over A (2) K-algebraic A is algebraically closed

IV, Definition 4.2, p. 192 IV, Definition 4.3, p. 197 IV, Exercise 4.6, p. 202 VII, Definition 1.11(2), p. 410 IV, Definition 1.2(5),pp. 155-156 111, Definition 6.1(2), p. 130

algebraically closed fdmost mtisymmetric a t (atomic) atomic

formula [type] is almost over A

Ax (axiom)

(A, &)-compact (1) B is F-atomic over A (2) atomic type (3) A is T-atomic over B atp (8, J , 4 , atp @ , I ) (1) Avd(1, A ) , Av(I, A ) (2) Av(D,A) (1) Ax(I)-Ax(XII)

automorphism

f ie an automorphism of M

based

(1) Z is based on A (2) I is based on p (3) a is based on W

atP Av (average)

baaic bi-set

(2) Ax(Al)-(E2)

bi-set function

V, Definition 7.1, p. 305 III, Definition 6.1(4), p. 130 111,Definition 2.1(1), (2), p. 94

I, Definition 2.5, p. 11

VI, Definition 1.5, p. 328 IV,Definition 1.5, p. 157

VI, Definition 1.4, p. 327 XI, Definition 2.2(2),p. 562 VII, Definition 2.2, p. 412 111, Definition 1.5, p. 89 VII, Definition 4.1(1), p. 426 IV, pp. 152-153, and Table 1, p. 169 XI,-pp. 562-565 I, Definition 1.4, p. 5 111, Definitionl.8, p. 90 111, Definition 4.3, p. 118 VI, Definition 3.7(3), p. 358 see Horn VII, Definition 1.8, p. 409

* Notice that for e.g., Av(Z, A), P ( p , A, A), strongly A-homogeneous,you should look at Av, D, homogeneous, reap. So look a t the main ward, ignoring strongly, explicitly, etc., but semi-, uni-, multi-, bi-, are considered part of the word. Note that the same word may have different meaning depending on the text (e.g., regular cardinal and regular type; Av(Z, A ) and Av(D, I)),whereas some variations are only shortening (e.g. P ( p , A, A), D(p,A, A)). So we number the distinct meanings. Some too well-known notions were omitted. 69 1

692

INDEX O F DEFINITIONS AND ABBREVIATIONS

Boolean ultrapower

Boolaan ultrapower N(m)/D VI, Definition 3.8, p. 369

V, Notation, p. 289 V, p. 290

C

cnat (conjunction of atomic) cer (orCard) cntegoricel

VI, Definition 1.6, p. 328

cb (CenoniCBl

V, Notation, p. 289 sea Introduction III, Theorem 6.10, p. 134

cc (chain

VI, Definition 3.7(3), p. 358

Cer K

b-4

condition) cdt (contradictory type) of (cofinality) cl (closure)

111, Definition 7.2, p. 141

closed compaot

complete

component connected

coneervative contradictory constructible construction contradictory

CP (combinetorial principle) CR (complete

-1

Ctp (canonical type)

(4) Ff-compact model (1) D is a A-complete filter (2) complete model (3) A-descending complete ultrefilter (4) complete type (6) complete theory M , is a

Notation, p. xxix 111,Definition 6.1(6), p. 130 V, Definition 4.4(6), pp. 277-278 IV, Definition 1.2(2), pp. 155-15 I, Definition 1.2(2), (3). p. 3 VI, Definition 1.6, p. 328 VII, Definition 1.4(2), p. 402 end MI,Definition 1.9, p. 410 IV,Definition 2.1(3), p. 157 VI, Definition 1.3(6), p. 326 Appendix, Definition 1.1(6), p. 653-654 VI, Definition 5.1, pp. 382-383 VI, Definition 6.2, pp, 391-392

(CPA.x.p. x. e)

see Notation see Notation XIII, Definition 3.1, I, Definition 2.5, p. lf 634 Appendix, Definition 3.2(l ) , P. 669 VII, Definition 2.1(2), p. 41 1 11, Definition 1.1(3)(i), p. 21 IV,Definition 1.3, p. 156 IT,Definition 1.2(1), p. 155 VIII, Definition 3.2, p. 464 Appendix, Definition 3.1, p. 666 see n-inconsistent XIII, Definition 2.2, p. 628

CR@, A)

11, Definition 3.4(1), p. 66

explicitly contredictory F-constructible F-construction (1) x-contradictory (2) strongly K-contradictory (3) n-contradictory

111, Theorem 6.10, p. 134

INDEX OF DEFINlTIONS AND ABBREVIATIONS

D (degree)

dcl (definable closure) DC decomposition

dcl(A)

11,Definition 3.2, p. 42 V,Definition7.2(1),pp.30&307 111, Definition 5.5, p. 127 Appendix, Definition 1.2, p. 654 111,Definition 6.1(3),p. 130

DC(I), DCW(I),D C W )

VII, Definition 1.10, p. 410

(1) (N,,, a,: q E I ) is a (T,&*)-

decomposition

(2) u

(T,C * ,A ) -

(4) u

(T,G*)-

decomposition (3) u (T,E * ) decomposition inside M

Ded

decomposition of M (1) Ded h

(2)Ded, h Dedekind deep definable, defined definable closure define definitional extension degree depend

depth didip (discontinuity dimensional Property1 divides df (definition) dim (dimension)

693

(A, p)-Dedekind cut

T is deep

p is definable over A, p is ($, A ) - d e h b l e , p is $-defined d is defined by a formula

CtYPel

(1)a formula depends on an equivalence relation (2)E depends on 0 mod Y (3) d depends on I (1) the depth of (N, N', a) (2)the depth of T T has the didip

XI,Definition 2.4(1),p. 565

XI,Definition 2.4(2),p. 565 XI,Definition 2.5(1),p. 566 XI, Definition 2.5(2),p. 566 Appendix, Definition 1.4, p. 657 Appendix, Definition 1.4, p. 490 VII, Definition 1.10,p. 410 X,Definition 4.2(2),p. 528 11, Definition 2.1, p. 31 see do1

111, Definition f3.1(1),p. 130

111, Theorem 5.14, p. 128 see D

111,Definition 2.1(1), p. 94

111, Definition 5.3,p. 124 111, Definition 4.4,p. 118 X,Definition 4.1,pp. 527-528 X,Definition 4.2(1),p. 528 X,Definition 2.6,p. 520

111,Definition 1.3, p. 85

11, Definition 4.5,p. 77

111, Definition 4.5(1), (2),(4), dim(p, B, A) p. 119 (3)dim(Z, A, M ) , d h ( 1 , A ) 111,Definition 3.3, p. 106

694

INDEX OY DEFINITIONS AND ABBREVIA'FIONS

Dom (domain) d0P (dimensional order property) DP

Dom P T has the dop

X, Definition 4.1, p. 527 X, Definition 4.2(1), p. 528 X, Definition 4.3(2), p. 528 X, Definition 4.3(3), p. 528 X, Definition 4.4A, p. 529 11, Definition 3.3, p. 44

ds (descending sequences) E

(1) E+

(2) E of a representation EC EC(To. F) ECN (equivalence ECN(Eo, @) class number) (1) Elementary submodel Elementary (2) (M, N)-elementary mapping EM'(1, a), EM'(I,N), EM EM1(I), EM(I, @), etc. (1) @Q,Tea,pea, MeQ eq (equivalences classes) (2) e q ( 4 (1)p is equivalent to q equivalent (2) J, Z are equivalent (3) elementarily equivalent (4)equivalent representations (1) (A, 2)-existenceproperty existence (2) T hes the (A, n)existence property (3) T has the true ( A , n)-existence Property (4) strong (X,, n)existence property extension property family f.c.p. FE (finitmy equivalences) filter

X, Definition 2.1, p. 512

111, Definition 6.5, p. 133 X, Definition 5.8, p. 536 VII, Definition 5.1(1), p. 432 111, Definition 5.2, p. 124 I, Definition 1.1, p. 2 I, Definition 1.3, p. 4 VII, Definition 2.6, p. 413; VII, Lemma 2.6, p. 415 111, Definition 6.2, p. 131 ; 111, Definition 6.3, p. 132 VI, Definition 4.2, p. 375 11, Definition 1.3, p. 23 111, Definition 1.6, p. 89 see Notation Definition 5.17B, p. 547

x,

XII, Definition 4.2, pp. 60&609 XII, Definition 5.2, p. 616 XII, Definition 5.4(1), p. 616 XII, Definition 5.4(2),p. 616

VII, Definition 2.9, p. 418

( A , K)-family

VII, Definition 1.11(1), p.

FEm(A)

11, Definition 4.1, p. 62 111, Notation, p. 94

(1) filter over I (2) trivial filter (3) principal filter

410

Appendix, Definition 1.1( I), p. 653 Appendix, Definition 1.1(2), p. 486 Appendix, Definition 1.1(6), pp. 653-654

INDEX OR' DEFINITIONS AND ABBREVIATIONS

finite cover Property FI (finite intersection) fork free freedom full function U

gap UE

GI

good

888

H

homogeneous

Horn

I

IE

incomplete inconsistent ind independence property

f.c.p.

F W ,FI,('3)

VI, Definition 3.6(2), p. 358

p forks over A S [(S, A)] is free [ ( T , , 2')free] [free in (T,, T)] (T,, T)has ( p , A)-freedom a full model ( A , a)-function

111, Definition 1.4, p. 85 VIII, Definition 1.2(1), (2), p. 445 VIII, Definition 1.2(3), p. 445 VI, Definition 6.2, p. 383 11, Definition 3.3, p. 44

QiwlJ,

Ml)

the main gap theorem GEi(M, N ) UIi(iV, M ) (1) good [K-goodl [h-good]model (2) good [A-good] filter; A-good Boolean algebra (3) A is a good set

h

695

h(9, v)

H(I) (1) homogeneous, K-hOmOg0neOUS (2) strongly K- homogeneous (3) A-model homogeneous (1) Horn formula (sentence) (2) basic Horn formula

VI, Definition 1.6, p. 328 XII,Theorem 6.1, p. 620 VIII, Definition 2.1, pp. 459-460 W I , Definition 2.1, pp. 45S460 V, Definition 6.1, p. 294

VI, Definition 2.1(1), (2), p. 333; VI, Exercise 3.16, pp. 354-355 XII, Definition 3.2, p. 604

VII, Definition 3.1, p. 422 V, Notation, p. 289 I, Definition 1.6, (I), p. 6 I, Definition 1.6(2), p. 6 VIII, Remark, p. 472. VI, Definition 1.2, p. 326 VI, Definition 1.2, p. 326 VIII, Definition l . l ( l ) ,(3), p. 444; IX, Definition 2.1, pp. 459-460; X, Definition 1.8(1), p. 511 X, Definition 1.8(2),p. 511 VIII, Definition 1.1(2), (3), p. 444 X, Definition 1.8(2),p. 511 X, Definition 1.8(2),p. 511 VI, Definition 1.3(6), p. 326 11, Definition 3.2(3)(ii),p. 43 11, Theorem 4.8(2), p. 72 11, Exercise 4.6, p. 80 11, Definition 4.2, p. 69

696

INDEX O F DEFINITIONS AND ABBREVIdTIONB

independence

indiscernible

inevitable inp (independent partitions) ird (independent orders) isolated isomorphic

(1) Z is independent over

III, Definition 4.4(1),

[over PI (2) I7 is independent over

ELI, Definition 6.4, p. 125

A , [over ( B ,4 1

@andmod!?' (3) Y is independent mod D (4) (31, gn,D)K-independent (1) ( A , n ) indiscernible (set of sequences), A-ni n b r n i b l e , n-in&oernible, eta. (2) (A, n)-indiecernible sequences, A-n-indiscernible, n-indiscernible (3) maximal indiscernible set (4) absolutely indiscernible (6) (A, n)-indiscernible indexed set, etc. ~ E S " ( Ais) inevitable K c p ( T ) , 'CindT), K r E p ,

T)

&d(T),

p. 118

(21,

VI, Definition 3.1, p. 345; VI, Definition 3.6, p. 358 VI, D W t i o n 3.3, p. 350 I, Definition 2.4, p. 10

I, Definition 2.3, p. 10

111, Definition 3.2, p. 106

IV,Definition 6.1, p. 212 VII, Definition 2.4, p. 413 IV, Definition 5.9A, p. 210

III,Definition 7.3, p.

145

-

111,Definition 7.1, p. 137

Kird(T)

is F-isolated over A M ,N are isomorphic

IV, Section 1, p. 153 I, Definition 1.4, p. 6

k

(1) k(N0,Nl) (2.1 k(N1)

K

(1) K = (2) K h

XIII, Definition 4.6(3), p. 647 XIII, Definition 4.7(1), p. 648 XIII, Definition 4.7(2), p. 648 V, Section 6, p. 289 V, Definition 6.2, p. 296 II,Definition 4.4(1), (3), p. 75

(3) k(T)

(3)

Keisler kind

Kr

L (hecar rank) I

P)

K m ,TI,W A ) , W A ) , K(A),etc.

(7) K i Keisler order @, @ A (1) Ba is the kind of d (2) (used only in X, $5) W ( A , T), K r y A ) , etc. L(P) (1) W 0 , N l ) (2)

large

(F,w,A,

W,)

v)

(3) J is a A-large ( < A-large) subtree

M, Definition 2.5, p. 413

X, Definition 4.1, pp. 527-528 X, Definition 4.3(1), p. 528 X, Definition 4.3(1), p. 528 VI, Definition 4.1, pp. 37&371 111, Definition 6.4, p. 132 X, Definition 5.16F, p. 545 11, Definition 4.4(2), (3), p. 75

V, Definition 7.6, p. 316 XIII, Definition 4.6(4), p. 648 XIII, Definition 4.7(2), p. 648 XIII, Definition 4.7(2), p. 648 X, Definition 5.8, p. 536

697

INDEX OF DEFINITIONS AND ABBREVIATIONS

lcf (lower cofinelity) 1gw limit ultrapower log (logarithm) low (lower weight)

MA (Martin's Axiom) minimal

Mlt mod (modulo) monotonic multidimeneional multiplicative multiplicity r)

narrow

ND (number of dimeneione) omit ord order property

orthogonal

hf(K,

D)

VI, Definition 3.6, p. 357

V,Definition 3.6(1),p. 261 lgw(P). lgw(& A ) the limit ultrapower M $ ( D VI, Definition 4.2, p. 375 log, m low(p), low&), low(U, A), V, Definition 3.4, p. 259; V, Definition 4.4(4),pp. 277-278 low*(&A ) , low&), l o w ~ (A 4) olementery mapping I, Definition 1.3, p. 4 (1)I a m x b l indis111, Definition 3.2, p. 106 cernible set over A in M (2)F - n ~ & ~ n a l V, Remark, p. 289 See [ndS 701 (1)M is F-minimal over A (2)weekly minimal formula (3)minimnl t p [indkcernible eet] (4)R-weaklyminimsl (6)A is T-minimal .over B UtYp, A, A), MltYp, A ) (2 is 1 or 2)

IV,Definition 4.4, p. 201

(1)multidimeneioml I (2) multidimeneioml T

V,Definition 5.2, p. 286 V, Definition 6.3,p. 286 VI, Definition 2.1(1),p. 333

V,Definition 1.3(3), p. 238 V, Definition 1.3(1), (2),

p. 238 V, Definition 7.2(3), pp. 306-307 XI, Definition 2.2(6), p. 563

II, Definition 1.2, p. 21 see depend

VI, Definition 2.1(1), p. 333

eee Mlt

(1) n(E) (number of the

111, Notation, p. 94 equivalence classes of E ) XIII, Definition 4.6(1), p. 647 (2) W W 4 ) XIII, Definition 4.7(1), p. 648 (3) n(NJ XIII, Definition 4.7(2),p. 648 (4) n(TJ A-narrow X, Definition 5.16A, p. 544 IX, Theorem 2.3, p. 502 ND(T)

(1)M omits a type (2) M Strongly omits 8 type P Tord

formula hae the order property (order p) (1)weekly orthogonal types

Notation

VI, Definition 6.3,p. 392 II, Theorem 4.8(1), p. 72

11,Theorem 2.2(3), pp. 30-31

V, Definition l.l(l), p.

230

698

INDEX OF DEFINITIONS AND ABBREVIATIONS

(2) orthogonal types,

orthogonal indiscernible

seh

otop (omitting type order property) perdel pertition

PC (pseudoelementary) power primery

V,Definition 1.1(2), (3), p.230

(3) p is orthogonal to B (4) p is stronglyorthogonal to 9 ( 5 ) p orthogonal to A (6)p is almost orthogonal to A T has the otop

V, Definition 4.4(2), p. 277 V, Definition 4.4(3), pp. 277-278

parallel types pertition of a Boolean algebra PC(T1, TI,PC,(TI, TI

111, Definition 4.2, p. 117 VI, Definition 3.7, p. 358

V, Definition 1.1(4),p. 230 X, Definition 1.5, p. 511

XII, Definition 4.1, p. 608

VI, Definition 6.2, p. 383; V I I , Definition 2.1(1), p. 411 see reduced power IV, Definition 1.4(1), p. 156

proper

set [model] is F-primary over A (1) model [set] is F-prime over A (2) M is prime over A for K (3) A is T prime over B (1) set [model] is Fprimitive over A, or (F, p)-primitive (2) M ( A )is primitive over AinK (3) A is T-primitive (1) reduced product (2) product of filters D , x Dl @ proper for (I,T)

qf (quantifier free) qd (quantifier depth)

(qf m)-type, compaot VI, Definition 1.5, p. 328 model qd,,; (qd,,,ml-type, compact VI, Definition 1.6, p. 328 model

prime

primitive

product

IV,Definition 1.4(3), p. 156 IV, Definition 1.6, p. 157 XI, Definition 2 . 2 ( 5 ) , p. 563 IV,Definition 1.4(2), p. 156

IV, Definition 1.8, p. 157 XI, Definition 2.2(4), p. 562 V, Definition 1.2, p. 233 VI,Definition 3.6, p. 358

VII, Definition 2.7, p. 414

R (r=w

11, Definition 1.1, p. 21

rank Ramsey Theorem

see

reduced power reduced product

R

Appendix, Theorem 2.1, p. 659 VI, Definition 1.1(3), pp. 324-325 VI, Definition 1.1(2), p. 324

INDEX OF DEFINITIONS AND ABBREVIATIONS

699

V, Definition 1.2, p. 233 V, Definition 3.1, p. 251

regular

V, Definition 3.6, p. 265

V, Definition 4.4(1), p. 277

V, Definition 4.6(4), (6),

regularize representation

(6)regular family of sets (7) D is A-regular [regular] filter ( 8 ) A is a regular cardinality family of sets regularize a filter (1) (N7, u V :~ € 1is) a representation (2) an F-representation (3) E of the representation (4)equivalent representation (5) standard representation

p. 278 VI, Definition 1,3(1),p. 326 TI, Definition 1.3(3), (4), p. 326 see Notation

VI, Definition 1.3(2), p. 326 X, Definition 5.2, p. 534; redefined X, 5.17, p. 547 X, Definition 5.3, p. 534 X, Definition 5.8, p. 536

X, Definition 5.17B, p. 547 X, Definition 5.8(2), p. 536

V, Definition 2.1(2), (3), p. 240

VII, Definition 1.2, p. 402

I, Definition 2.1(2), (3), P. 9

(2) (F, p)-saturated (3) F-semi-saturated (4)F-aturated (6)(A, H I , H2)-saturated model (6) (A, &saturated model

sct

SE

I, Definition 1.2(1), (3), P. 3 IV, Definition l.l(l), p. 155 IV,Definition 1.1(3),p. 155 IV,Definition 1.1(4), p. 155 VII, Definition 1.4(l), p. 402; W, Definition 1.9, p. 410 VII, Definition 1.6,p. 403; see VII, Section 1 I, Definition 1.5, p. 6 XI, Definition 2.2(1), p. 562 111, Definition 7.6, p. 149 XIII, Definition 4.1(1), pp. 643-644 XIII, Definition 4.1(2), p. 644 XIII, Definition 4.1(3), p. 644 XIII, Definition 4.1(3), p. 644 VII, Definition 4.1(2), (3), p. 426

700

INDEX OF DEFINITIONS AND ABBREVLILTIONS

semi-minimel

(1) semi-minimaltype (2) semi-minimalformula (3) strongly semi-minimal

V, Definition 4.1, pp. 267-269 V. Definition 4.3, pp. 276-277 V, Definition 4.3, pp. 276-277

semi-regular

(1) semi-regular type (2) P-semi-regular type

V, Definition 4.1,

semi-simple semi-weaklyminimal set shallow simple

formula

a formula is semi-weakly-

minimal set function H,pure set function H T is shallow (1) B-simple type

(2) strongly 9-simple type

skeleton Skolem

S M ) (special number of dimensions) split

I, Definition 2.6, p. 11

111, Definition 1.2, p. 85 111, Definition 7.4, p. 145 (1) stable theory (in A), stable model (in A),

I, Definition 2.2, p. 9 11, Theorem 2.13, p. 36

(2) ~(3, $)-stable formula (in A) (3) A-atomicallystable (1) stable system

11, Theorem 2.2(1), p. 30

(2) sp. etable system

standard stationarkat ion stationary

X, Def. 4.2(2), p. 528 V, Definition 4.6(1), (6), p. 278 V,Definition 4.6(2), (6), p. 278 VI, Definition 4.6, p. 377 VIII, Definition 3.1, p. 464 VII, Definition 1.1, p. 400

XIII, Definition 4.1(1), pp. 643-6

A-stable

stable system

VII, Dsfinition 1.3, p. 402

XIII, Definition 4.6(2), p. 647 XIII, Delinition 4.7(1), p. 648 XIII, Definition 4.7(2), p. 648

and

srd (strict independent partitions) stable

p. 267 V, Definition 4.6(3), p. 278 V, Definition 4.6, p. 278 V, Definition 4.2, p. 274

(3) true sp. stable system the representation is standard q is the stationarization of p over A (1) p is stationary over A (2) p is stationary

VII, Definition 2.8, p. 415 XII, Definition 2.1, p. Uefinition 5.1, p. XII, Definition 5.1, p. XII, Definition 5.3, p.

598 ; 616 616 616

X,Definition 5.8(2),p. 536 111, Definition 4.2(2), p. 117 111, Definition 1.7, p. 90 111, Definition 4.1, p. 117

VII, Definition 4.1(6), p. 426

INDEX OF DEFINITIONS AND ABBREWATIONS

(3) S

StP strict order property Rubmodel superstable supported system

c

A is stationary

(4) p is stationary inside A (5) p is stationary inside (B,A) (1) stp(4 A ) (2) stp*(& A ) , stp*(d, A ) formula q(Z;5) (theory T ) has the strict order Property (1) elementary submodel (2) submodel superstable theory T

70 1

Appendix, Definition 1.3, p. 655 XI, Definition l . l ( l ) , p. 557

XI, Definition 1.1(2),p. 557 111, Definition 2.1, (3), p. 94 111, Definition 2.1(3), p. 94 11, Definition 4.3, p. 69 I, Definition 1.1, p. 2 Notation I, Definition 2.2(6), p. 9 VI, Definition 3.7(2), p. 358 me. stable system

T Tarski-Vaught

VIII, Lemma 1.3, p. 445 XI, Definition 3.1(5),p. 573

Th (theory) tP (type)

Notation I, Definition 2.1(1), (3), p. 9

TP TPC TPS TPX transcendental tree

111, Definition 1.1, p. 85 VII, Definition 1.6, p. 406 see TPX aee TPX VII, Definition 1.7, p. 406 TPX"(a,M) (1) transcendental T II,Definition 3.4(2), p. 66 (2) totally transcendental T 11, Definition 3.1, p. 41 VII, Definition 3.1, p. 422 (1) (5, Bl-tree (2) strong tree VII, Definition 3.2, p. 423 (3) uniform &tree V I I , Definition 3.2, p. 423 a trival type X, Definition 7.1, pp. 55&551 III, Definition 3.3, p. 106 true dimension IX, Definition 1.1, p. 492 'J!VZ(O, A )

trival true W (TarskiVaught) type

q-type, n - t m e , Fff-t-0

W , Definition 2.1(1), p. 157

ugw

UgW(P),urn@. A )

V, Definition 3.5; p. 261 Appendix, Deihtion 1.1(3), p. 653-654 VI, Definition 1.1(3), pp. 324-325 VI, Definition 1.1(3), pp. 324-325 VI, Definition 8.1, p. 390 V, Definition 2.2. p. 247 VI, Definition 3.4, p. 355 I, Definition 1.8, p. 6

ultrafilter ultrapower ultraproduct UL (ultralimit) unidimensional

uniform

universal unstable unsuperetable

W M , D, 4 uniform filter universal, A-universal, ( < A)-universel model negation of stable negation of superstable

702

INDEX OF DEFINITIONS AND ABBREVIATIONS

4

UPW

UPW(P), UPW@,

w (weight)

(1) W ( P ) l

w (weakly)

I I,J,P

W

(1) set of triples (2) WE

(upper weight)

winning strategy witness ZFC (ZermeloFraenkel with choice)

(2)

%(P)9

n-witness

4%A ) wI?(4A )

swq

V, Definition 3.3, p. 259

V, Definition 3.2, p. 252; 888 V, Theorem 3.9, p. 254 V, Definition 7.2(2), pp. 306-307 V, Definition 2.1(1), (3),

p. 240 V, Section 6, p. 289 V, Claim 7.1, p. 306 VI, Definition 1.6, p. 328; VIII, Definition 2.1, p. 459 V, Definition 7.3, p. 309