Comfort W.W., Negrepontis S. — The Theory of UltraFilters :: Электронная библиотека попечительского совета мехмата МГУ

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Comfort W.W., Negrepontis S. — The Theory of UltraFilters

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Название: The Theory of UltraFilters

Авторы: Comfort W.W., Negrepontis S.

Аннотация:

An ultrafilter may be considered as a finitely additive measure. In this view, every subset of X is either considered "almost everything" (has measure 1) or "almost nothing" (has measure 0).

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 497

Добавлена в каталог: 09.02.2014

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Предметный указатель

Monk, D.      201 380
Monotone      217 252
Morel, A.C.      162 163 284 285 309 311 379
Morley, M.      80 82 99 100 140 201 285 312
Morley, theorem of      275
Mostowski, M.      19 80
Mrowka, S.      162
Multiplicative      217 252
Nachbin, L.      60
Nakamura, M.      308
Natural number      8
NEAR      355
Negrepontis, S.      60 80 81 140 141 163 203 231 232 261 309 340 378 379 380 408 409 452
Neighborhood      22
Nikodym, O.M.      162
Noble, N.      80
Non-comparable      4
Normal space      22
Normal ultrafilter      188
Novak, J.      379
Olin, P.      379
Open partion      383
Order of ramification system      167
Order topology      31
Order-isomorphism      4
Order-type      9
Ordered pair      2
Ordinal (number)      5
Ordinal sum      9
Ordinal, cofinality of      14
Ordinal, even      9
Ordinal, finite      8
Ordinal, limit      8
Ordinal, non-limit      8
Ordinal, odd      9
P(a) [in partially ordered set]      3 167
Parovicenko I.I.      140 201 379 408
Partial order      3
Partial order of Rudin — Frolik      430
Partial order of Rudin — Kreisler      206
Partially ordered set      3
Partially ordered set, compatible elements of      74
Partially ordered set, countable chain condition in      75
Partially ordered set, filter in      74
Partition      211
Partition of an element      179
Partition, $\alpha$ -      222
Partition, open      383
Partition, refinement of      180
Peano axioms      8
Permutation      206
Piccard, S.      261
Pierce, R.S.      60 80 201 380
Pincherle, S.      311 339
Pitt, R.A.      450
Plank, D.      409
Point-homogeneous      136
Pondiczery, E.S.      81
Pospisil, B.      162 163
Power set axiom      2
Pre-order      3
Pre-order of Rudin — Frolik      430
Pre-order of Rudin — Kreisler      206
Prikry, K.      162 165 201 203 286 309 380
Principle of definition by transfinite recursion      9
Principle of proof by transfinite induction      4
Problem of Souslin      74
Produce      450
Product of filters      157
Product, reduced      269
Projective space      50
Proof by induction      263
Property $(H_{\alpha})$       119
Property $(R_{\alpha})$       124
Property $[p,G,\alpha]$       344
Property $\Phi_{\alpha}$       223
Pseudobase      58
Pseudobase, uniform      290
Pseudocompact      402
Pseudoweight      58
pw(X)      58
Quasi-normal ultrafilter      212
Rado, R.      20 61 75 79 80 164 201
Rado, theorems of      62 174 175
Radon, J.      162
Rainwater, J.      60
Rajagopalan, M.      380
Ramifiable cardinal      167
Ramification system      167
Ramification system, order of      167
Ramsay, A.      140 379
Ramsey cardinal      165
Ramsey ultrafilter      189
Ramsey ultrafilter, strongly      190
Ramsey, F.P.      164 200
Ramsey, theorem of      174
Realcompact      402
Recursion, definition by      263
Reduced product      269
Reduct      272
refinement      180 288 383
Regr      291
Regressive      291
Regular ultrafilter      149
Regular-open subset      52
Relation $\tau(i)$ -ary      82
Relation, anti-symmetric      3
Relation, binary      2
Relation, connected      3
Relation, reflexive      3
Relation, transitive      3
Relational system(s)      82
Relational system(s), cardinality of      83
Relational system(s), embedding of      83
Relational system(s), isomorphism of      83
Relational system(s), similar      83
Relational system(s), subsystem of      83
Remote point      407
Restriction set      68
retract      50
Retract of Boolean algebra      49
Riesz, F.      59
Robinson — Craig joint consistency theorem      272
Robinson, A.      285
Ross, K.A.      80
Rothberger, F.      379
Rowbottom, F.      81 165 202 203 231
Rowbottom, theorems of      189 190 191
Rubin, H.      19
Rubin, J.E.      19
Rucker, R.V.B.      162 339
Rudin — Frolik (pre-)order      430
Rudin — Kreisler (pre-)order      206
Rudin, M.E.      61 81 140 231 232 261 410 450 451
Rudin, W.      140 163 231 379 451
Ruziewicz, S.      261
S(X)      66
Sanin, N.A.      75 79 80
Satisfiable      277
Satisfiable, finitely      277
Satisfies      264
Saturated      277
Schoenflies, A.      19
Schreier, O.      100
Schroeder, E.      379
Scott, D.      162 163 165 201 202 203 284 285 309 311 379
Scott, theorems of      188 191
Selective ultrafilter      210
Selective ultrafilter, uniformly      210
Semadeni, Z.      162

Sentence      263
Separates elements      28
Set      1 see
Set, free      249
Set, regressive      291
Sevee, D.      100 285
Shelah, S.      61 81 233 261 309 312 339 340 379
Shelah, theorem of      333
Sierpinski, W.      19 20 115 140 162 286 308
Sikorski, R.      59 60 201 309 408
Sikorski, theorem of      49
Silver, J.H.      162 202 203
Similarity type      82
Simpson, S.G.      201
Singleton      2
Skolem, Th.      19 284 311
Slomson, A.B.      285
Smith, E.C.      201
Solomon, R.C.      451
Solovay, R.M.      19 74 75 80 81 162 202 286 308 309
Solovay, theorem of      295
Souslin Line      74
Souslin number      66
Souslin's problem      74 80
Souslin, M.      61 74 75 80 81
Souslin-homogeneous      66
Space      21
Space perfect      118
Space, $F_{\alpha}$ -      343
Space, $\alpha$ -basically disconnected      350
Space, $\alpha$ -co-homogeneous      132
Space, $\alpha$ -co-universal      132
Space, $\alpha$ -compact      181
Space, $\mathcal{B}$ -compact      383
Space, $\sigma$ -compact      22 402
Space, basically disconnected      350
Space, compact      22
Space, extremally disconnected      50
Space, F-      343
Space, normal      22
Space, point-homogeneous      136
Space, projective      50
Space, pseudocompact      402
Space, realcompact      402
Space, totally disconnected      40
Space, zero-dimensional      42
Special structure      84
Special structure, elementarily      276
Special structure, existence of      96
Special structure, uniqueness of      94 96
Specializing chain      84 99
Specker, E.      200 342 380
Specker, theorem of      370
Stavi, J.      309
Steiner, A.K.      379 451
Steiner, E.F.      379 451
Stepanek, P.      80 309
Stepping-up lemma      174
Stone extension      27
Stone space      40
Stone topology      40
Stone — Cech compactification      24
Stone's duality      46
Stone, A.H.      80
Stone, M.H.      59 60
Strongly compact cardinal      196
Strongly discrete      226 429
Strongly measurable cardinal      196
Structure      82
Structure for $L(\tau)$       263
Sub-type      332
Sub-uniform ultrafilter      364
Subalgebra      33
Subalgebra generated by      33
Subbase, $\alpha$ -subbase      31
Subformula      263
Subset, coinitial      103
Subset, completely separated      22
Subset, d-thick      424
Subset, dense      53 58 74 110
Subset, directed downwards      118
Subset, directed upwards      118
Subset, free      249
Subset, homogeneous      165 212
Subset, regressive      291
Subset, regular-open      52
Subset, retract      50
Subset, strongly discrete      226 429
Subset, subspace, cofinal      103
Supremum      3
Szpilrajn, E.      79
Tarski, A.      20 59 60 80 81 161 162 200 201 202 231 284 286 308 312 380
Tarski, definition of      264
Tarski, recursion formula of      17
Tarski, theorems of      67 266
Tennenbaum, S.      74 75 80
Th, $Th(\mathfrak{A})$       265
Theory of $\mathfrak{A}$       265
Thick      424
Tietze's extension theorem      22
Totally disconnected      40
Transfinite induction, principle of proof by      4
Transfinite recursion, principle of definition by      9
Tychonoff product theorem      28
Tychonoff product theorem, analogue of      183
Tychonoff, A.      59
Type of an element      206
Type, elementary      265
Type, elementary open set      120 343
Type, elementary relational system      82
Type-equivalent      205
Ulam Matrix      197 203
Ulam, S.      59 202 203
Ulam, theorem of      197
Ulam-measurable cardinal      196
Ulmer, M.D.      80
Ultrafilter      143
Ultrafilter, $(\kappa, \gamma)$ -regular      148
Ultrafilter, $\beta$ -descendingly incomplete      198
Ultrafilter, $\delta$ -uniform (on $\mathfrak{A}^{\delta}$ )      253
Ultrafilter, $\kappa$ -complete      145
Ultrafilter, $\kappa$ -uniform      144
Ultrafilter, $\kappa$ -uniformly selective      210
Ultrafilter, adequate      259
Ultrafilter, Alexander's property      181
Ultrafilter, countably incomplete      145 252
Ultrafilter, descendingly incomplete      197
Ultrafilter, Eklof property of      304
Ultrafilter, fine      232
Ultrafilter, good      217 252
Ultrafilter, non-principal      144
Ultrafilter, norm of      144
Ultrafilter, normal      188
Ultrafilter, principal      144
Ultrafilter, quasi-normal      212
Ultrafilter, Ramsey      212
Ultrafilter, regular      149
Ultrafilter, selective      210
Ultrafilter, strongly Ramsey      190
Ultrafilter, sub-uniform      364
Ultrafilter, ultrapower modulo      269
Ultrafilter, ultraproduct modulo      269
Ultrafilter, uniform      144
Ultrafilter, uniform over $\alpha$ -partition      223
Ultrafilter, uniformly selective      210
Ultrafilter, weakly Ramsey      212
Ultrapower      269
Ultraproduct      186 269
Uniform closure      223
Uniform finite intersection property      144

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