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| Goldblatt R. — Topoi |
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| Предметный указатель |
Order-relation on N 345
Order-relation on the continuum 424ff.
Ordered pair 18
Ordinal 33
Pairwise compatible 362 376 390 391
Partial arrow 268
Partial Arrow Classifier Theorem 269
Partial element 268
Partial function 268
Partial order 29
Partial section 290 291
Partial transitivity 330
Partial, object of, elements 270
Parts of a space 435
Path 193
Peano postulates 347ff. 424
Point 435 477
Point, less 437
Points have enough- 436 478
POSET 29 42
Positive-existential 493 502
Potential existence 274
Power objects 104
powerset 76
Powerset axiom 308
Powerset functor 195
Powerset, contravariant 197
Precanonical pretopology 473 510
Predecessor arrow 342
Predecessor function 339
Preorder 28
Preserves 459f.
Presheaf over a category 375
Presheaf over a space 359
Pretopology 374
Pretopology, canonical 473
Pretopology, precanonical 473 510
Primitive recursion 335ff.
Primitive recursion Theorem 339
Principal crible 370
Principal hereditary set 213
Product, fibred 65
Product, finite 52
Product, m-fold 52
Product, m-fold, arrow 47
Product, m-fold, as adjoint 442
Product, m-fold, category 34
Product, m-fold, category of objects 47
Product, m-fold, set 19 46
Projection 46 53
Proof sequence 131
Provably epimorphic 507
Provably equivalent 505
Pseudo-complement 179
Pseudo-complement, relative 181
Pseudo-complemented lattice 179
Pullback 63
Pullback as fibred product 95
Pullback lemma 67
Pullback, preserves epics 115
Pullback, square 64
Pulling-back functor 449
Pulling-back functor, adjoints to 449 450 452
Pushout 68
Pushout, monic, as pullback 355
Quantifier axioms 238
Quantifier, existential 231
Quantifier, universal 231
Quantifiers arrows 245
Quantifiers as adjoints 453ff
Quotient as co-equaliser 62
RANGE 19
Real numbers 413ff.
Realisation 235
Recursion, primitive 335ff.
Recursion, primitive, on well-founded relations 318—320
Recursion, simple 302
Recursive arrow 321
Reduction Theorem 475
Reflects 45 9f.
Reflexive 28 61
Regular HA-element 381 503
Regularity axiom 312
Relation 18 310 322
Relation, equivalence 61
Relation, extensional 317
Relation, inverse 45
Relation, kernel 66
Relation, membership 6 103 315 327
Relation, order 345
Relation, well-founded 317—318
Relative pseudo-complement 181
Relative pseudo-complement as adjoint 444
Relatively pseudo-complemented lattice 182
Replacement axiom 312
Representable functor 449
Representation 26
Restriction 65
Restriction of a to p 389
Restriction of s to p 283
Restriction of s to U 360
Restriction, ordering 390
Richard Nixon 27
Right exact 461
Right-cancellable 39
Rigid  -set 406
Rigid equality 406
Ring 516ff.
Rules of Inference 131
Russell set 9
Russell's paradox 9
S-topos 467
Satisfaction 236 239
Satisfaction in -Set 285
Satisfaction in Set 257
Section 94
Section, continuous 98
Section, global 98 267
Section, local 98
Section, partial 290 291
Section, partial, of an epic 290
Selection 362
Selection, disjoint 408
Sentence 126
Sentence, first-order 235
Sentence, PL 130
Separation, bounded 309
Separation, bounded, axion 308
Separation, bounded, principle 11
Sequent 496
Sequent, geometric 496
Set 6
Set as a topos-object 334
Set membership 6
Set vs. class 10
Set, - 276
Set, complete - 388
Set, empty 7
Set, hereditary 189
Set, object 326
Set, power 76
Set, product 19 46
Set, Russell 9
Set, singleton 44
Set, theory 6
Set, transitive 313
Set, transitive, object 321
Set, variable 212
| Set, varying with time 219
Sheaf 96 97
Sheaf of continuous functions 388 392
Sheaf of germs of open sets 97 369
Sheaf of sections 362 389
Sheaf of truth-values 400
Sheaf over 391
Sheaf, - 395
Sheaf, flabby 403
Sheaf, j- 379
Sheaf, pre- 359 375
Sheafification 465 470
Sieve 206
SIMPLE 406
Simple sheaf 406
Simple, 2- 411
Singleton 44
Singleton, -subset 282 388
Singleton, forming arrow 269
Site 375
Site, elementary 378
Site, finitary 481
Site, small 469
Skeletal category 42
Skeleton 201
Small class 466
Small site 469
Small, locally 466
Sober 435
sort 483
Soundness Theorem for  -validity 186 249
Soundness Theorem for B-validity 135
Soundness Theorem for CL 132
Soundness Theorem for GL 498
Soundness Theorem for HA-validity 185
Source 17
Spatial topos 97
Spatial СНА 436
Splitting epic 290
Stack over a category 375
Stack over a space 359
Stalk 90
Stalk as colimit 363
Stalk space 90
Standard model 307
State of knowledge 188
Strict 280
Strong arrow 395
Sub-extensional object 410
Subcategory 32
Subcategory, full 33
Subobject 76
Subobject, classifier 81
Subobject, classifier, as free object 448—449
Subobjects, lattice of 151
Subset 8
Substitution lemma 250 4!
Subtraction 342
Successor arrow 302
Successor function 301
Sufficient 477
Sum of objects 54
Support 291—292
Surjective arrow 124
Surjective function 39
symmetric 61
TARGET 17
Tautology 129
Term 234
Terminal object 44
Theorem see Completeness Diaconescu's Fundamental Partial Primitive Soundness Validity
Theory 492 496
Theory, consistent 499
Theory, geometric 493
topology 420
Topology on a topos 378
Topology, discrete 406
Topology, double negation 379
Topology, forcing 515f.
Topology, generated 515
Topos, - 467
Topos, bivalent 118
Topos, Boolean 156
Topos, classical 118
Topos, classifying 514
Topos, coherent 481
Topos, defined over 467
Topos, disjunctive 171 229
Topos, elementary 84
Topos, extensional 169
Topos, Grothendieck- 376 469
Topos, S- 467
Topos, spatial 97
Topos, well-pointed 116
Transitive closure 314
Transitive relation 28 61
Transitive representative 328
Transitive set 313
Transitive set-object 321
TREE 313
TRUE 80 81
Truth Lemma 259
Truth-arrows 139
Truth-arrows in Set 221
Truth-functions 127—128
Truth-values, classical 126
Truth-values, object of 162
Truth-values, sheaf of 400
Union of sets 7
Union of subobjects 147
Union, disjoint 54
Unit of adjunction 440
Unit of adjunction, со- 440
Universal arrow 441
Universal construction 58
Universal instantiation 238
Universal property 58
Universal quantifier 231
Universe of sets 333
Upper bound 55 179
Valid - 141 249
Valid  - 382
Valid  -formula 237
Valid BA- 135
Valid H- 185
Valid P- 189
Valid, B- 35
Valid, classically 130
Validity Theorem 224
Valuation 135 141 185 189 382
Value assignment 130
Variable bound 235
Variable set 212
Variable set as sheaf 366
Variable, free 235
Variable, individual 231 234
Weak arrow 395
Weak, forcing 381
Weakly extensional category 293
Weakly extensional object 409
Weakly linear poset 192
Well-defined concept 62
Well-founded relation 317 318
Well-pointed 116
Yoneda embedding 471 473 511
Yoneda functor 470
Yoneda, lemma 470
ZF 11 312 333
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