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

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Предметный указатель

Theory, $\textbf{ZC}\vartheta$       124
Theory, $\textbf{ZFCI}$       299
Theory, $\textbf{ZFC}$       21
Theory, $\textbf{ZFC}[\textbf{J}]$       307 309
Theory, $\textbf{ZFC}\vartheta$       49
Theory, $\textbf{ZFC}\vartheta^{+}$       160
Theory, $\textbf{ZFC}_{\kappa}[*]$       311
Theory, $\textbf{ZFGC}$       148
Theory, $\textbf{ZFGT}$       166
Theory, $\textbf{ZFGT}^{weak}$       148
Theory, ${ }^{o}\textbf{HST}$       237
Theory, ${\textbf{BIST}$       88
Theory, internal      84
Theory, internal core interpretable      181
Theory, nonstandard      133
Theory, reducible      133
Theory, standard      133
Theory, standard core interpretable      133
Theory, “realistic”      135
Thin (equivalence relation)      371
Transitive      16
Transitive closure      44
Transitive extension      237
Transitive, over      237
Transversal      37

TREE      191
Tree, well-founded, wf      192
Truth T, truth predicate      119
Truth, truth set      119 169
TYPE      274
T[y]      194
U, $\mathcal{F}$ -quotient power      141
U, $\mathcal{F}$ -quotient power, “definable”      163
Ultrafilter      140
Ultrafilter, C-adequate      143
Ultrafilter, countably incomplete      143
Ultrafilter, Fubini product      150
Ultrafilter, good      143
Ultrafilter, regular      143
Ultrafilter, ultrafilter U      7 163
Uniformize      344
Union, $\cup$ X      21
Universe $\textbf{V}$ , universe of $\textbf{ZFC}$       42
Validation function      48
Well-founded core      134
X      141 141
[f]      141
“External power set”      104
“planar” (set)      340
“realistic” theory      135
“V = L”      159

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