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| Goldblatt R. — Topoi |
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| Предметный указатель |
 -topos 467
Abstraction 25
Abstraction, functional 288
Action, empty 117
Action, empty, of a monoid 100
Action, empty, preserving function 101
Actual existence 274
Addition on  335
Addition on N 337
Adjoint, left 439
Adjoint, right 439
Adjoint, right, situation 438.
Adjunction 439
Adjunction, co-unit of 440
Adjunction, co-unit of, in posets 446
Adjunction, unit of 440
Algebra of classes 125
Algebra of classes, Boolean 134
Algebra of classes, Brouwerian 178
Algebra of classes, closure 178
Algebra of classes, Heyting 183
Alphabet for elementary languages 234
Alphabet for PL 129
and-Or map 420
Antecedent 132
antisymmetric 29
Apartness 425
Appropriate to  239 484
Appropriate to t 484
arrow 23 24
Arrow in  -Set 277
Arrow, category 34
Arrow, name of 78
Arrow, partial 268
Arrow, strong 395
Arrow, weak 395
Associative law 21 24
atom 481
Atomic formula 234
Atomic sentence 483
Axiom of Choice 290—301 312
Axiom of extensionality 307
Axiom of infinity 311
Axiom of null set 308
Axiom of order-completeness 421
Axiom of pairs 308
Axiom of partial transitivity 330
Axiom of patching for sheaves (COM) 362 376 391
Axiom of powersets 308
Axiom of regularity 312
Axiom of replacement 312
Axiom of separation 308
Axiom of transitive representation 328
Axiom of transitivity 314
Axiom of unions 308
Axioms for CL 131 237 238
Axioms for continuous functions 427
Axioms for Dedekind cuts 415 423 427 430
Axioms for geometric modality 382
Axioms for GL 497
Axioms for identity 238
Axioms for IL 177 249
Axioms for propositional logic 131
Axioms for quantifiers 238
Axioms for set theory 307ff.
bar 193
Barr's Theorem 482 495
Beth model 193 388
Bi-complete 69 466 469
Biconditional 274
Bijective 39
Bivalent 118
Boolean algebra 134
Boolean topos 156
Bound variable 235
Bounded frame 191
Bounded functor 470
Bounded IL-model 191
Bounded ite 386
Bounded lattice 133
Bounded protopology 471
Bounded separation 309
Brouwerian algebra 178
Bundle 89
Canonical  -model 487
Cartesian closed category 72
Cartesian product 19
Cartesian square 64
Categories, equivalent 200
Categories, functor 202
Categories, ismorphic 200
Category 24
Category as first-order concept 232
Category, arrow 34
Category, comma 35
Category, degenerate 72
Category, discrete 30
Category, one-object, (monoid) 32
Category, opposite 45
Category, preorder 28
Category, product 34
Category, skeletal 42
Category, sub- 32
Cauchy-reals 414 418
Chain 72
Change of variables 505
CHARACTER 81
Characteristic arrow 81
Characteristic function 79
Choice function 290
class 10
Class, abstracts 309ff
Class, proper 10
Classical Completeness Theorem 498 512
Classical logic 131
Classical topos 118
Classifier 81
Classifying topos 514
Closure algebra 178
Closure operator 372
Co-complete 69
Co-equaliser 60
Co-free 441
Co-unit 440
Codomain for arrow 24
Codomain for function 17
Cofinality 386
Coherent topos 481
Cokernel 114
Collapsing Lemma 317
Comma category 35
Commutative diagram 21
Commutativity of addition 338
Compact space 481
Compactness Theorem 500 502
Compatible 361 376 390 391
Compatible family 472
Complement of lattice element 134
Complement of set 7
Complement of subobject 147
Complement, pseudo 179
Complement, relative pseudo 181
Complemented lattice 134
Complete -set 388ff
Complete category 69
Complete Heyting algebra 276
Complete model 404
Complete, bi- 69
Complete, finitely 69
Complete, order- 421
| Complete, со- 69
Completeness Theorem for -validity 227 265
Completeness Theorem for BA and B-validity 136
Completeness Theorem for CL 132
Completeness Theorem for HA-validity 185
Completeness Theorem for poset (frame)-validity 191
Completeness Theorem Goedel's 238
Completeness Theorem Infinitary 502
Completeness Theorem, Classical 498 512
Completion of an -set 393—397
complex numbers 423
Component (of a natural transformation) 199
Composition of arrows 24
Composition of functions 20
Composition of functors 198
Comprehension and descriptions 288
Comprehension for -sheaves 405
Comprehension, and 107
Comprehension, principle of 6
Cone 58
Conjunction 126
Conjunction, truth-arrow 139
Conjunction, truth-function 127
Connectives 126
Consequent 132
Conservative functor 461
Consistent 12
Constant 231
Constructivism 173ff.
Continuous, function as generalised real number 427
Continuous, morphism 473
Continuous, section 98
Continuously variable real number 417
Continuum Hypothesis 381
Contravariant functor 196
Contravariant hom-functor 197
Contravariant powerset functor 197
Copower 413 469
Coproduct 54
Coproduct as adjoint 443
Coproduct, arrow 54 55
Coproduct, preserves pullback 115
Covariant functor 196
Cover 374
Cover, open 361
Crible 208 368 376
De Morgan's law 423 434
Decidable ordering 425
Dedekind-reals 414ff.
Dedekind-reals as continuous functions 416
Dedekind-reals in  -Set 419 421
Dedekind-reals in -Set 416 421
Dedekind-reals, *R equals - 434
Degenerate category 72
Deligne's Theorem 481 495 512
Deligne's Theorem, proof of 500
Denned over 467
Dense monic 372
Dense monic, j 379
Density of  434
Descriptions 287
Descriptions, interpreted in sheaves 404
Detachment 131
Diaconescu's Theorem 297
Diagram 58
Diagram, commutative 21
Diagram, empty - 59
Diagram, finite 69
Direct image part 464
Directed poset 192
Discrete category 30
Discrete topology 406
Disjoint arrows 119
Disjoint selection 408
Disjoint sets 54
Disjoint union 54
Disjunction 126
Disjunction, truth-arrow 139
Disjunction, truth-function 128
Disjunctive topos 171 229
Distributive lattice 134
Domain of arrow 24
Domain of function 17
Double Negation 184 379
Duality 45
Duality principle 46
Effectively epimorphic 472
Element of a set 6
Element of an object 78
Element, existing 274
Element, global 398
Element, partial 268
Elementary, language 231 234
Elementary, logic in a-Set 284
Elementary, site 378
Elementary, topos 84
Empty action 117
Empty diagram 59
empty function 43
Empty section 283
Empty set 7
Empty, non- 115
Endo arrow 445
Enough points 436
Epi-monic factorisation 114
Epic arrow 39
Epic arrow, splitting 290
Epimorphic family 471
Epimorphic family, effectively 472
Epimorphic family, provably 507
Equaliser 56
Equaliser, monic as 109
Equality 274
Equality as local equality 385
Equality of set-objects 326
Equality, rigid 406
equation 487
EQUIVALENCE 274
Equivalence class 61
Equivalence of categories 200
Equivalence of set-models and topoi 328ff
Equivalence relation 61—63
Equivalence, logical 144
Equivariant function 101
Evaluation arrow 70 71
Exact functor 461
Exact functor, Left 461
Exact functor, Right 461
Examples of adjoint situations 442ff
Examples of categories 26—36
Examples of elementary sites 379
Examples of functors 195ff
Examples of Heyting algebras 179—183
Examples of limits 59—60
Examples of monoid actions 101
Examples of natural transformations 199—200
Examples of pseudo-complements 179
Examples of pullbacks 64—68
Examples of relative pseudo-complements 181
Examples of sites 375
Examples of topoi 85—103
Examples of truth-arrows 139—140
Examples of variable sets 219
Excluded Middle 161
Excluded Middle and Intuitionism 175
Existence, actual 274
Existence, degree of 275
Existence, equals local existence 387
Existence, potential (partial) 274
Existence, predicate 267
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