Kanovei V.G., Reeken M. — Nonstandard Analysis: Axiomatically :: Электронная библиотека попечительского совета мехмата МГУ

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Kanovei V.G., Reeken M. — Nonstandard Analysis: Axiomatically

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Название: Nonstandard Analysis: Axiomatically

Авторы: Kanovei V.G., Reeken M.

Аннотация:

The book is devoted to nonstandard set theories that serve as foundational basis for nonstandard mathematics. Several popular and some less known nonstandard theories are considered, including internal set theory IST, Hrbacek set theory HST, and others. The book presents the basic structure of the set universe of these theories and methods to effectively develop "applied" nonstandard analysis, metamathematical properties and interrelations of these nonstandard theories between each other and with ZFC and some variants of ZFC, foundational problems of the theories, including the problem of external sets and the Power Set problem, and methods of their solution. The book is oriented towards a reader having some experience in foundations (set theory, model theory) and in nonstandard analysis.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 432

Добавлена в каталог: 11.04.2008

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

Предметный указатель

      10 24
      161
$<_{B}$       362 380
$<_{CD}$       362 380
$<_{G}$       168
$<_{\xi}$       151
$A\cdot\mathcal{B}$       324
$a^{put}[G]$       261
$A^{S}_{x}$       296
$a_{x}$       192
$B(\prod^{0}_{\varepsilon})$       331
$B(\prod^{1}_{n})$       331
$B(\Sigma^{0}_{\varepsilon})$       331
$B(\Sigma^{1}_{n})$       331
$Base(2^{I})$       321
$c/\mathbb{N}$       364
$CD(\mathcal{A})$       327
$Clop(\mathcal{X})$       321
$c\mathbb{N}$       364
$C^{fin}$       143
$Def_{\epsilon, st}^{'}(P)$       220
$DI_{x}$       195
$D^{t}$       275
$E_{p}$       102
$Form(\mathfrak{L}, \mathfrak{M}, \Phi)$       48
$Form_{\textbf{G}}$       166
$Fun \textit{f}$       164
$F_{t}$       192
$f_{x}$       140
$ht_{H}$       258
      143
$irk { }\textit{x}$       44
$j_{xy}$       199 202
$L_{\mu}$       352
$M_{U}$       37 378
      261
$Nms_{o}$       261
$Nms_{\xi}(P)$       261
$p { }^{\bullet}= g$       184
$p { }^{\bullet}\in q$       184
$p\circeq q$       106
$p\Phi$       275
$p^{t}(x^{t})$       275
$Q_{U}iR(i)$       325
$rank \textit{x}$       42
$sh_{\mathcal{A}}$ ”X      329
$sh_{\mathcal{A}}(x)$       329
$st_{\textit{f}} x$       225
$Succ_{T}(t)$       191
$sup^{S} X$       190
$s\wedge t$       191
$S_{\kappa}$       151
$Truth_{G}$ T, modified truth predicate      169
$T_{x}$       192
$T|_{a}$       193
$T|_{t}$       193
$U\circ\{V_{i}\}_{i\in{ }I}$       326
$U\textit{i}\Phi(\textit{i})$       141
$U^{C}$       326
$V_{\xi}$       42
$V_{\xi}[U]$       44
$x \simeq y$       54
$x \varepsilon p$       184
      195
$x^{(H)}$       258
$X^{<\lambda}$       33
$X^{<\omega}$       27 220
$X^{C}$       321
$X^{Y}$       10
$X^{\lambda}$       33
$X_{\alpha}$       167
$x|_{t}$       193
$y_{k}$       160
$[x]^{a}$       211
$[\Phi]$       142
$\aleph_{1}$       321
$\aleph_{\xi}$       25
$\alpha$       202 211
$\alpha_{k}$       160
$\cap(I)$       325
$\check{x}$       258
$\chi_{u}$       325
$\circ$       326
$\cup X$       21
$\cup(I)$       325
$\Delta^{0}_{0}[\mathcal{X}]$       321
$\delta_{a}$       263
$\epsilon$       141
$\epsilon$ -isomorphism      132
$\epsilon$ —structure      46 132
$\equiv_{B}$       362 380
$\equiv_{CD}$       362 380
$\exists^{bd}$       111
$\exists^{int}$       14
$\exists^{st}$       14
$\exists^{wf}$       16
$\exists^{\infty \lg}$       58
$\forall^{bd}$       111
$\forall^{int}$       14
$\forall^{stfin}$       85
$\forall^{st}$       4 14
$\forall^{wf}$       16
$\forall^{\infty \lg}$       58
$\infty$       144
$\lceil ... \rceil$       132
$\leq_{B}$       362 380
$\leq_{CD}$       362 380
$\lozenge(t_{1}, ..., t_{k})$       274
$\mathbb{B}$       111
$\mathbb{E}[\textit{f}]$       245
$\mathbb{HF}$       28
$\mathbb{HF}$ in $\textbf{EEST}$       190
$\mathbb{H}$ , a model of $\textbf{HST}$       258
$\mathbb{H}$ -class      260
$\mathbb{H}[G]$       261
$\mathbb{I}^{(\nu)}$       180 184
$\mathbb{I}_{0}$       258
$\mathbb{I}_{k}$       230
$\mathbb{I}_{k}$ in IST and BST      111
$\mathbb{L}[\mathbb{I}_{k}]$       248
$\mathbb{L}[\textit{f}]$       245
$\mathbb{N}$       26
$\mathbb{N}$ -sequence      307
$\mathbb{N}[\textit{w}]$       223 224
$\mathbb{N}_{M}[w]$       224
$\mathbb{P}$ , product forcing      280
$\mathbb{P}^{(\alpha)}$       203
$\mathbb{P}_{i}$       280
$\mathbb{P}_{\mathfrak{L}(\mathfrak{A}, \mathfrak{B})}$       276
$\mathbb{Q}$       54
$\mathbb{R}$       54
$\mathbb{S}(c_{1}, ..., c_{n})$       89 221
$\mathbb{S}(X)$       221
$\mathbb{S}[\textit{w}]$       89 221 222
$\mathbb{S}^{(v)}$       134
$\mathbb{S}_{M}[w]$       224
$\mathbb{WF}$       16
$\mathbb{WF}[U]$       44
$\mathbb{WF}[\textit{f}]$       239
$\mathbf{P}_{i}$       281
$\mathcal{D}$       170
$\mathcal{F}/U$       141
$\mathcal{F}^{P}$       150
$\mathcal{F}^{s}$       150
$\mathcal{P}(X)$       10 21 23
$\mathcal{P}_{ext}(X)$       104
$\mathcal{P}_{fin}(X)$       27
$\mathcal{P}_{int}(X)$       23 32
$\mathfrak{A}_{i}$       280
$\mathfrak{B}_{i}$       280

$\mathfrak{C}[D]$       275
$\mathfrak{L}(k)$       280
$\mathfrak{L}(\mu)$       352
$\mathfrak{L}^{\infty}$       275
$\mathfrak{L}_{i}$       280
$\mathfrak{L}_{\in, st, int}$       290
$\mathfrak{M}\models\Phi$       10 48
$\omega, \aleph_{0}, \aleph_{1}$       10 25
$\omega_{1}$       321
$\omega_{\xi}$       25
$\Phi[G]$       266
$\Phi[i]$       142
$\Phi\bullet K$       331
$\Phi\{A_{i}\}$       325
$\Phi^{int}$       14
$\Phi^{q}$       46
$\Phi^{st}$       14
$\Phi^{wf}$       16
$\Phi^}{bd}$       111
$\Pi^{0}_{\epsilon}[\mathcal{X}]$       321
$\Pi_{1}^{\blacksquare\blacksquare}$       33
$\Pi_{2}^{\blacksquare\blacksquare}$       33
$\prod^{0}_{0}[\mathcal{X}]$       321
$\prod^{0}_{<\xi}$       348
$\sum^{0}_{0}[\mathcal{X}]$       321
$\sum^{0}_{\varepsilon}[\mathcal{X}]$       321
$\sum^{\blacksquare\blacksquare}_{1}$       34
$\sum^{\blacksquare\blacksquare}_{2}$       34
$\textbf{A}(\textit{f})$       245
$\textbf{A}(\underline{\textit{f}})$       245
$\textbf{E}$       184
$\textbf{L}(k)$       280
$\textit{e}$       184
$\textit{i}$       291
$\textit{s}$       291
$\textit{w}$ -st x      223
$\textit{w}-st_{M}$ x      224
$\texttt{TRUE}(\mathfrak{M}, \Phi)$       48
$\theta(Z, x, Y)$       116 118
$\times_{p\in P}U_{p}$       150
$\underline{A}$       197
$\varepsilon$       184
$\varepsilon(r)$       364
$\varphi^{\nu}$       141
$\Xi(n, x)$       164
$\|A\|$       282
$\|f\|$       150
$\|x\|$       149
${ }^{*}card X$       25
${ }^{*}st$       141
${ }^{*}V=\langle { }^{*}V; { }^{*}\varepsilon, { }^{*}st\rangle$       141
${ }^{*}\mathbb{N}$       26
${ }^{*}\mathbb{Q}$       54
${ }^{*}\mathbb{R}$       54
${ }^{*}\textit{w}$       16
${ }^{a}=$       199
${ }^{a}int x$       199
${ }^{a}int$       199
${ }^{a}st x$       199
${ }^{a}st$       199
${ }^{a}x$       193
${ }^{a}\in$       199
${ }^{a}\Phi$       202
${ }^{e}x$       103
${ }^{int}2^{H}$       321
${ }^{o}x$       56
${ }^{S}X$       15
${ }^{s}\{x\in X: \Phi(x)\}$       85
${ }^{Y}X$       10
${ }^{\bullet} =$       184
${ }^{\bullet}int p$       184
${ }^{\bullet}int$       184
${ }^{\bullet}st p$       184
${ }^{\bullet}st$       184
${ }^{\bullet}\in$       184
${ }^{\bullet}\Phi$       185
${ }^{\sigma}X$       14 85
${ }^{\sigma}\mathbb{N}$       90
      192
$|T|^{*}$       197
$|t|^{*}_{T}$       197
$|t|^{S}_{x}$       296
$|t|_{T}$       192
$|\pi|$       280
$|\vdash_{C}$       282
*-rational      54
*-real      54
=      141
A      324 325
A-code      192
Absolute formula      23
Absolute operation      23
Absolute set      23
Alephs      25
Algebra      321
Asterisks      16
atom      304
Axiom of costructibility      159
Axiom, $BST^{int}$       182
Axiom, $ZFC^{st}$       14 84
Axiom, $\kappa$ -Boundedness      241
Axiom, $\kappa$ -deep BI      105
Axiom, $\kappa$ -size BE      138
Axiom, $\kappa$ -size BI      105
Axiom, Basic Enlargement      87
Axiom, Basic Idealization      86
Axiom, Bounded Inner Transfer      125
Axiom, Choice      21
Axiom, Choice, $2^{k}$ -size Choice      241
Axiom, Choice, c-size      319
Axiom, Collection      21
Axiom, comprehension      20
Axiom, Dependent Choice      19
Axiom, Enlargement      86
Axiom, Extensionality      20
Axiom, Global Choice      148 303
Axiom, Idealization      85
Axiom, III-founded Mostowski Collapse      303
Axiom, Infinity      21
Axiom, Inner $\kappa$ -Boundedness      105
Axiom, Inner Boundedness      86
Axiom, Inner Standardization      85
Axiom, Inner Strong $\kappa$ -Boundedness      105
Axiom, Inner Transfer      84
Axiom, Internal Size Collection      298
Axiom, Minimality      159
Axiom, Pair      20
Axiom, Parametrization      182
Axiom, power set      21
Axiom, Regularity      21
Axiom, Regularity over      0 15
Axiom, Replacement      21
Axiom, Saturation      19
Axiom, Saturation, $\kappa$ -deep      241
Axiom, Saturation, $\kappa$ -size      241
Axiom, Separation      20
Axiom, SMA      294
Axiom, Special Model Axiom      294
Axiom, Standard Condensation      297
Axiom, Standard Size Choice      19
Axiom, Standard Size Collection      297
Axiom, Standardization      15
Axiom, SuperUniversality      303
Axiom, Transfer      15
Axiom, Transitivity of      0 15
Axiom, union      21
Axiom, Universality      303
Axiom, “ $\mathbb{H}=\mathbb{L}[\mathbb{I}]$ ”      214
A[G]      261
B-smooth      381

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