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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$(H_{\alpha})$       119
$(R_{\alpha})$       124
$(\prod_{i \in I} X_{i})_{(\kappa)}$       69
$2^{\alpha}$ , $\alpha^{\kappa}$       12
$<\kappa, \mathcal{H}>$ -large oscillation mod $\mathcal{F}$       325
$=_{\mathcal{F}}$       37
$a^{+}$ , $b^{-}$ [in $\Lambda(\alpha)$ ]      108
$C/\mathcal{F}$ , $C(\xi)$       328
$d:\alpha \rightarrow \alpha \times \alpha$       159
$ess.sup_{p}\{ \beta_{\xi}:\xi <\alpha \}$       300
$e_{*}:\mathfrak{A}^{\beta}/q \rightarrow \mathfrak{A}^{\alpha}/p$       337
$F/\mathcal{F}$       154
$f^{-1}$       2
$G(\alpha)$       400
$h:X\rightarrow S(\mathfrak{B}(X))$       41
$K^{+}(\alpha)$ , $K^{-}(\alpha)$       113
$L_{C}$       264
$Mon(\alpha, h)$       253
$Mon(\alpha, \mathcal{F})$       253
$Mult (\alpha, h)$       253
$Mult(\alpha, \mathcal{F})$       253
$N(\alpha)$       370
$P(\alpha)$       223
$P_{\alpha}$ -point, P-point      30 135
$P_{\alpha}$ -space, P-space      30
$P_{\alpha}(X)$       135
$R\ K(\alpha)$       400
$S(\alpha, \kappa)$       287
$S(\mathfrak{B})$       39
$S(\phi):S(\mathfrak{B}) \rightarrow S(\mathfrak{A})$       46
$SU(\alpha^{+})$       364
$S_{\alpha}$       133
$t:\beta \times \alpha \rightarrow \alpha \times \beta$       157
$U(\alpha)$ , $U_{\kappa}(\alpha)$       144
$U_{\alpha}$ , $L_{\alpha}$ , $\Delta_{\alpha}$       159
$X_{(\kappa)}$       69
$X_{\alpha}$       31 69
$[p, G, \alpha]$       344
$[\alpha]^{\kappa}$       15 289
$\alpha \rightarrow (\kappa)^{<\omega}_{\lambda}$       190
$\alpha \rightarrow (\kappa)^{n}_{\lambda}$       165
$\alpha$ -*saturated      317
$\alpha$ -*universal      317
$\alpha$ -Baire category property      134 393
$\alpha$ -basically disconnected      350
$\alpha$ -co-homogeneous      132
$\alpha$ -co-universal      132
$\alpha$ -compact      181
$\alpha$ -complete      177
$\alpha$ -directed      92
$\alpha$ -embedding      176
$\alpha$ -generated      182
$\alpha$ -good      252
$\alpha$ -homogeneous      86 99
$\alpha$ -partition      222
$\alpha$ -partition, uniform over      223
$\alpha$ -representable      177
$\alpha$ -representable, weakly      179
$\alpha$ -saturated      277
$\alpha$ -subbase      31
$\alpha$ -universal      86 99
$\alpha$ -universal, elementarily      274
$\alpha^{+}$       15
$\alpha^{\underline{\kappa}}$       15
$\approx$       205
$\bar{c}$       264
$\bar{f}$ , $\bar{g}$       27 206
$\beta(\alpha)$       24
$\beta(\alpha)$ , $\beta(X)$       24
$\bigvee_{i \in I} \mathcal{B}_{i}$       384
$\bigwedge$ , $\bigvee$       49
$\bigwedge_{i \in I} \mathcal{A}_{i}$       180
$\cap$ , $\cup$ , $\subset$ , \      2 3
$\cdot$ [cardinals]      12
$\cdot$ , $\times$ [filters]      156
$\chi$ , $\chi(p)$ , $\chi(p,X)$       152
$\cong$       83
$\delta_{\alpha}$       159
$\emptyset$       2
$\equiv$       265
$\equiv_{P}$       186
$\eta_{\alpha}$ -set      103
$\in$ , =, $\neg$ , $\wedge$ , $\exists$ , $\vee$ , $\rightarrow$ , $\forall$       1 261
$\kappa$ -almost disjoint family      286
$\kappa$ -product topology      69
$\kappa^{-}$       280
$\Lambda(\alpha)$       105 398
$\le$ [Boolean algebra]      34
$\le$ [functions]      217
$\le$ [ordinals]      7
$\le_{p}$       186
$\ll \ \gg$ , $\ll C \gg$       33
$\ll$       168
$\log \alpha$       78
$\lor$ , $\wedge$       32
$\mathbb{0}$ , $\mathbb{1}$ [in $\Lambda(\alpha)$ ]      105
$\mathbb{0}$ , $\mathbb{1}$ [in $\mathfrak{B}$ ]      32
$\mathbb{2}$       36
$\mathbb{BA}$       116
$\mathbb{C}$       15
$\mathbb{I}(\mathbb{C})$ , $\mathbb{I}(\mathbb{K}_{\alpha})$ , $\mathbb{I}(\mathbb{P}_{\alpha}^{\mathbb{K}}(\mathfrak{A}))$       84
$\mathbb{M}$ , $\mathbb{M}(Th(\mathfrak{A}))$       265
$\mathbb{O} n$       8
$\mathbb{O} \mathbb{S}$       101
$\mathbb{R}$       21
$\mathbb{T}$       206
$\mathbb{V}$       2
$\mathcal{B}$ -compact      383
$\mathcal{C}^{(\alpha)}$       31
$\mathcal{E}$       384
$\mathcal{E}^{'}$       392
$\mathcal{F}$ -satisfiable in $(\mathfrak{A}^{\alpha}/\mathcal{F})_{C/\mathcal{F}}$       328
$\mathcal{I}(C,\eta)$       384
$\mathcal{J}$ , $\mathcal{J}(X)$       31
$\mathcal{P}$ , $\mathcal{P}(\alpha)$       2
$\mathcal{P}^{\kappa}(\alpha)$       144
$\mathcal{P}_{\kappa}(\alpha)$       15
$\mathcal{Z}(X)$       22
$\mathfrak{B}(f):\mathfrak{B}(Y) \rightarrow \mathfrak{B}(X)$       46
$\mathfrak{B}(X)$       36
$\mathfrak{B}/\mathcal{F}$       37
$\mathfrak{C}(\alpha)$       337
$\mathfrak{C}_{a}$       118
$\mathfrak{C}_{a}$ , existence and uniqueness of      131
$\mathfrak{C}_{\alpha}$       118
$\mathfrak{H}_{\alpha}$       103
$\mathfrak{H}_{\alpha}$ , existence and uniqueness of      112
$\mathfrak{I}_{0}$ , $\mathfrak{I}_{\xi}$       16
$\mathfrak{I}_{\xi}(\alpha)$       174
$\mathfrak{L}(\alpha)$       108
$\mathfrak{P}(\kappa)$       322
$\mathfrak{R}(X)$       52
$\mathfrak{U}(\alpha)$       108
$\models$       264
$\models_{a}$       265
$\nu_{\alpha}$ -set      103
$\omega$       8
$\Omega_{\kappa}(\alpha)$       197 371
$\overline{A}$       22 121
$\parallel \ \parallel$ , $\parallel p \parallel$       144
$\phi :\beta(\alpha \times \beta) \rightarrow \beta(\alpha) \times \beta(\beta)$       157
$\Phi(L(\tau))$ , $\Phi_{n}(L(\tau))$       263
$\Phi_{\alpha}$       223
$\pi_{0},\pi_{1}:X \times Y \rightarrow X,Y$       156
$\prec$ [elementary substructure]      265
$\prec$ [refinement]      288 383
$\preceq$ [ $\beta(\alpha)$ , $\mathbb{T}(\beta(\alpha))$ ]      206
$\preceq$ [ $\mathcal{P}(\omega)/\mathcal{P}^{\omega}(\omega)$ ]      355
$\preceq$ [ $\tau$ $\preceq$ $\tau_{\alpha}$ ]      322
$\preceq$ [Boolean algebra]      180

$\prod_{\xi<\alpha}\mathfrak{A}_{\xi}/\mathcal{F}$ , $\mathfrak{A}^{\alpha}/p$       269
$\psi :\mathfrak{B} \rightarrow \mathcal{P}(S(\mathfrak{B}))$       40
$\sigma$ -compact      22 402
$\sqsubseteq$       430
$\subset$       2
$\sum$ , $\prod$       12
$\tau :X \rightarrow \mathbb{T}(X)$       206
$\tau$ , $\tau(U)$       120 343
$\tau(U)$       120 343
$\tau_{\alpha}: \alpha \rightarrow \omega$       322
$\uparrow$ [reduct]      272
$\uparrow$ [trace]      288 393
$\widehat{A}$       45 150
$\widehat{\mathfrak{B}}$       54
$\xi$ , $\xi(a,b)$       105 168
+      8 9 12
0,1,2,3...      8
< [ordered set]      103
<>, $<\mathcal{F}>$       37 234
Adequate ultrafilter      259
Adler, A.      162
Ailing, N.L.      100
Alexander's property      182
Alexandrov, P.      408
Almost disjoint family      286
Almost disjoint family, $\kappa$ -      286
Almost disjoint family, maximal      287
Amalgamation property      84 274
Anti-chain      4
Anti-symmetric      3 206
Anti-well-ordered      4
Arhangel'skii, A.V.      451
Aronszajn, N.      200 342
Aronszajn, theorem of      370
Arrow relation      165
Arrow relation, $\alpha \rightarrow (\kappa)^{<\omega}_{\lambda}$       190
Arrow relation, $\alpha \rightarrow (\kappa)^{n}_{\lambda}$       165
Artin, E.      100
atom      118
Atomic formula of $L(\tau)$       262
Automorphism      83
Ax, J.      340
Axioms of set theory      2 3
Bachmann, H.      19
Baer, R.      60
Baire category property      134 393
Balcar, B.      232 309
Balcar, theorem of      295
Banach, S.      60 201 382
Basically disconnected      350
Basically disconnected, $\alpha$ -      350
Baumgartner, J.E.      308 380
BD      22 399
Bell, J.L.      285
Benda, M.      339 380
Bernstein, F.      379
Beth cardinal      16 175
Blass, A.R.      163 231 232 233 261 340 408 450
Blass, theorems of      228 244 339
Bockstein, M.      79
Boolean algebra      22
Boolean algebra embedding      34
Boolean algebra, $\alpha$ -complete      176
Boolean algebra, $\alpha$ -distributive      178
Boolean algebra, $\alpha$ -representable      177
Boolean algebra, atomless      118
Boolean algebra, Boolean subalgebra of      33
Boolean algebra, canonical embedding of      54
Boolean algebra, canonical homomorphism for      38 177
Boolean algebra, complete      49
Boolean algebra, completely generated      295
Boolean algebra, completion of      54
Boolean algebra, condition ( $H_{a}$ ) in      119
Boolean algebra, condition ( $R_{a}$ ) in      124
Boolean algebra, dense in      53
Boolean algebra, filter of      37
Boolean algebra, greatest lower bound in      49
Boolean algebra, homomorphism      34
Boolean algebra, improper      32
Boolean algebra, injective      49
Boolean algebra, isomorphism      34
Boolean algebra, least upper bound in      49
Boolean algebra, partition of      180
Boolean algebra, proper      32
Boolean algebra, quotient      38
Boolean algebra, retract of      49
Boolean algebra, Stone duality for      46
Boolean algebra, Stone, space of      40
Boolean algebra, ultrafilter of      39
Boolean algebra, weakly $\alpha$ -representable      179
Booth, D.D.      231 261 410 450 451
Borel, E.      311
Bound variable      263
Bounded in $\mathbb{R}$       22
Bourbaki, N.      59
Brouwer — Kleene order      168
Brouwer, L.E.J.      200 408
Bukovsky, L.      80
C(X), C*(X)      22
C*-embedded      22
C-embedded      22
Canonical base $\mathcal{E}$ for $(2^{\alpha})_{\alpha}$       384
Canonical base $\mathcal{E}^{'}$ for $(\alpha^{x})_{x}$       392
Canonical base for $(\prod_{i \in I}X_{i})_{(\kappa)}$       69
Canonical embedding $(X \rightarrow \beta X)$       24
Canonical embedding $(\mathfrak{A} \rightarrow \mathfrak{A}^{\alpha}/p)$       271
Canonical embedding $(\mathfrak{B} \rightarrow \mathfrak{R}(S(\mathfrak{B})))$       54
Canonical homomorphism      38 177
Canonical projection $G(X) \rightarrow X$       57
Cantor set      133
Cantor — Bernstein theorem      2 12
Cantor, G.      19 20 82 99 100 101 114 308
Cantor, theorem of      104
Cardinal (number)      11
Cardinal of $L(\tau)$       263
Cardinal of relational system      83
Cardinal product      12
Cardinal sum      12
Cardinal, Alexander's property      182
Cardinal, beth      16 175
Cardinal, cofinality of      14
Cardinal, countable      12
Cardinal, finite      12
Cardinal, Hausdorff      165
Cardinal, infinite      12
Cardinal, limit      15
Cardinal, measurable      186
Cardinal, non-limit      15
Cardinal, ramifiable      167
Cardinal, Ramsey      165
Cardinal, real-measurable      203
Cardinal, regular      14
Cardinal, singular      14
Cardinal, strong limit      16
Cardinal, strongly $\kappa$ -inaccessible      62
Cardinal, strongly compact      197
Cardinal, strongly inaccessible      18
Cardinal, strongly measurable      197
Cardinal, Ulam-measurable      196
Cardinal, weakly compact      181
Cartan, H.      59
Cartesian product      2 3
Catczynska-Kartowicz, M.      80 81
Cauchy, A.L.      20
Cech, E.      59
Cellular family      66
CH, GCH      18
Chain      4 83
Chain, continuous      83
Chain, elementary      266

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