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Goldblatt R. — Topoi
Goldblatt R. — Topoi



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Название: Topoi

Автор: Goldblatt R.

Язык: en

Рубрика: Математика/Алгебра/Теория категорий/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-е издание

Год издания: 1984

Количество страниц: 568

Добавлена в каталог: 23.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\Omega$-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 $\mathscr{E}$      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 $\Omega$-sets      390
Join in posets      133
Kan extension      465
Kernel, pair      111
Kernel, relation      66
Kripke semantics for $\mathscr{L}$      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 $\Omega$-Set      284
Model of $\phi$      237 487
Model, $\mathscr{E}$-, for $\mathscr{L}$      246 484
Model, Beth      193 388
Model, classical, for $\mathscr{L}$      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 $\omega$      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 $R_d$      423 43Iff.
Order-relation on $\Omega$-sets      390
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