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| Goldblatt R. — Topoi |
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| Предметный указатель |
Existential as least upper bound 278
Existential generalisation 238
Existential quantifier 231
Exponential adjoint 71—72 444
Exponential in relatively pseudo-complemented lattices 187
exponentiation 70—71
Exponentiation as adjunction 444
Extension 211
Extensional  -subset 280
Extensional object 409
Extensional relation 317
Extensional topos 169
Extensional, sub - 410
Extensional, weakly 293 409
Extensionality, axiom of 307
Extensionality, principle 8
Extensionality, principle, for "parts" 436
Extensionality, principle, for arrows 116
Extensionality, principle, for subobjects 169
extent 284 389
Faithful functor 460
FALSE 117
Fibre 90
Fibred product 65 95
Finitary methods 12
Finitary site 481
Finite diagram 69
Finite products 52
Finite, ordinal 33
Finitely complete category 69
First-order concept 232
First-order language 231 234
Fixed point 123
Flabby sheaf 403
Forcing topology 515f.
Forgetful functor 195
Formula 234
Formula, geometric 493
Formula, infinitary 502
Formula, open 235
Formula, positive, existential 493 502
Foundations 13
Foundations, topoi as 332
Fragment 503
Frame 189
Frame, canonical 191
Free for t 237
Free over an object 441
Free, logic 267
Free, variable 235
Freyd Postulates 352ff
Function 17 310
Function, antitone 197
Function, bijective 39
Function, characteristic 79
Function, evaluation 70
Function, identity 19
Function, inclusion 19
Function, injective 37
Function, monotone 195
Function, partial 268
Function, surjective 39
Functional abstraction 288
functor 194
Functor categories 202
Functor, conservative 461
Functor, contravariant 196
Functor, covariant 196
Functor, exact 461
Functor, faithful- 460
Functor, forgetful 195
Functor, pulling-back 449
Functor, representable 449
Functor, Yoneda 470
Functors, isomorphic 199 202
Fundamental Theorem of Topoi 96 451
Generates 286
Generators 475
Generic model 514
Geometric field 517
Geometric modality 382
Geometric morphism 464
Geometric morphism over  467
Geometric theory 493
Geometric, surjective, morphism 467
Germ 90
Germ of a section 363
Germ of an open set 98 383
Global element 398
Global membership 316
Global section 98 267
Goedel's completeness theorem 238
Graph of arrow 457
Graph of function 18 20
Greatest element 179
Greatest lower bound 49 276
Grothendieck topology 385
Grothendieck topos 376 469
Group 41
Henkin method 499
Hereditary set 189
Hereditary set, principal 213
Heyting algebra 183
Heyting algebra, complete 276
Heyting-valued set 276
Heyting-valued set, complete 388
Heyting-valued set, rigid- 406
Higher-order language 231
Higher-order, logic 286
Hom-functor 196
Hom-functor, contravariant 197
Hom-set 196
Homeomorphic 41
Homeomorphism, local 97
Homomorphism, monoid 195
Identity arrow 25
Identity function 19
Identity Law 22 25
Identity of a monoid 31
Identity symbol 232
Image of a function 19
Image of a subobject 320
Image of an arrow 110ff.
Image, inverse 65
Implication 128 162
Implication, truth-arrow 139
Implication, truth-function 128
Impredicative definition 175
Inclusion function 19
Inclusion of relations 322
Inclusion of subobjects 76
Index of a formula 237
Infinitary formulae 501f.
Infinity, axiom of 311
Inhabited 428
Initial object 43
Initial object as adjoint 442
Injection 54
Injective arrow 124
Injective function 37
Intension 212
Intersection of sets 7
Intersection of subobjects 147
Intuitionism 175ff.
Intuitionistic logic 177 249
Inverse image 65
Inverse image part 464
Inverse of an arrow 40
Inverse relation 45
Invertible 40
| Iso arrow 40
Isomorphic categories 200
Isomorphic functors 199 202
Isomorphic objects 41
Isomorphic subobjects 77
Isomorphism 41 42
Isomorphism, defined up to 47
Isomorphism, natural 199
Isomorphism, unique up to 42
Iterate of an arrow 337
j-dense 379
j-sheaf 379
Join in -sets 390
Join in posets 133
Kan extension 465
Kernel, pair 111
Kernel, relation 66
Kripke semantics for  256ff.
Kripke semantics for PL 187ff.
Kripke-Joyal semantics 386
Kronecker delata 243 251
Language for modal logic 382
Language for propositional logic 129
Language, first-order 231 234
Language, higher-order 231
Language, many-sorted- 483
Lattice 55
Lattice as category 133
Lattice of subobjects 151
Lattice, bounded 133
Lattice, complemented 134
Lattice, distributive 134
Lattice, pseudo-complemented 179
Lattice, relatively pseudo-complemented 182
Least element 179
Least, upper bound 55 179 276
Left exact 461
Left ideal 102
Left-cancellable 38
Left-multiplication 100
Lemma, Mostowski's Collapsing 317
Lemma, Pullback 67
Lemma, Substitution- 250
Lemma, Truth 259
Lemma, Yoneda 470
LIMIT 58
Limit, point 384
Lindenbaum Algebra for CL 136
Lindenbaum Algebra for IL 185
Lindenbaum's Lemma 191
Local character of truth 387
Local equality 97 383
Local existence equals existence 387
Local homeomorphism 97
Local operator 373
Local section 98
Local set theory 316
Local truth 383 384
Locally constant function 365 407
Locally equal 97 363 385
Locally equal equals equal 385
Locally small 466
Locally true 97 99 365 372 383
Logic, classical 131
Logic, intermediate 228
Logic, intuitionistic 177 249
Logic, modal 187 381
Logically equivalent 144
Logicism 174
Lower bound 49
Lower semilattice 49
M-set 101
Many-sorted language 483
Maximal element 44
Maximum 44
Meet 133
Member 6
membership 6
Membership for set-objects 327
Membership in a topos 315 327
Membership of subsets of A 103
Membership tree 313
Metalanguage 306
Metaset 307
Minimal element 43
Minimum 43
Modal logic 187 381
Modal operator 385
Model for set theory 305ff.
Model in -Set 284
Model of  237 487
Model, -, for 246 484
Model, Beth 193 388
Model, classical, for 235
Model, complete 404
Model, generic 514
Model, P-based 189 256
modus ponens 132
Monad 383
Monic arrow 38
Monic arrow as equaliser 109
Monic arrow, dense 372
Monoid 31 100
Monoid action 100
Monoid homomorphism 195
Monoid identity 31
Mostowski's Collapsing Lemma 317
Multiplication on  339
Multiplication on N 346
Name of an arrow 78
Natural isomorphism 199
Natural map 62
Natural number 334
Natural numbers object 301ff.
Natural numbers object as free object 445 446
Natural numbers object in Sh(I) 365
Natural numbers object in Top(I) 304
Natural transformation 199
Negation 126
Negation, double 184 379
Negation, truth-arrow 139
Negation, truth-function 127
Neighbourhood 384
Non-empty object 115
Non-zero object 115
Object language 306
Object of partial elements 270
Object of truth-values 162
Object, extensional 409
Object, initial 43
Object, natural numbers 301ff.
Object, power 104
Object, set 326
Object, sub-extensional 410
Object, terminal 44
Object, transitive set 321
Object, zero 44
One object category (monoid) 32
One-one 37
Onto 39
Open as 'part' 435
Open cover 361
Open formula 235
Open set 96
Opposite arrow 45
Opposite category 45
Order-completeness 421
Order-completeness of *R 432 433
Order-completion of  423 43Iff.
Order-relation on -sets 390
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