Tourlakis G.J. — Lectures in Logic and Set Theory: Mathematical Logic :: Электронная библиотека попечительского совета мехмата МГУ

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Tourlakis G.J. — Lectures in Logic and Set Theory: Mathematical Logic

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Название: Lectures in Logic and Set Theory: Mathematical Logic

Автор: Tourlakis G.J.

Аннотация:

This two-volume work bridges the gap between introductory expositions of logic (or set theory) and the research literature. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly lecture style that makes them equally effective for self-study or class use. Volume I includes formal proof techniques, applications of compactness (including nonstandard analysis), computability and its relation to the completeness phenonmenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2003

Количество страниц: 328

Добавлена в каталог: 29.11.2009

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Предметный указатель

$(a)_{a\in M}$       95
$(iz)\mathcal{Q}$       120
$(z)_{i}$       240
$(\exists a \in M)...$       62
$(\mu x)$       128
$A\approx B$       104
$a\not\approx0$       107
$a^{\mathfrak{M}},f^{\mathfrak{M}},P^{\mathfrak{M}}$       53
$D(\mathfrak{A})$       88
$f:A\rightarrow B$       25
$i^{{\o}}$       77
$L(\mathfrak{M})$       54
$L_{\mathfrak{M}}$       54
$TH(\mathscr{C})$       76
$W_{a}$       143
$x\ast y$       137 165
$\bigcirc$       166
$\bigtriangleup$       166
$\Delta$       150
$\Delta_{n}$       151
$\Delta_{\infty}$       151
$\dot{-}$       131
$\exists!$       113
$\exists$ -introduction      36
$\forall$ -introduction      43
$\forall\exists$ -theory      93
$\Gamma+\mathscr{A}$       48
$\kappa$ -categorical      97
$\lambda$       125
$\lambda$ -notation      125
$\langle a_{0},...,a_{n-1}\rangle$       165
$\langle t[i]:i<w\rangle$       239
$\langle...\rangle$       19
$\lim_{x\rightarrow a^{+}}f(x)=b$       108
$\mathbb{N}$       15
$\mathbb{Q}$       15
$\mathbb{R}$       15
$\mathbb{Z}$       15
$\mathbf{Cl}(\mathscr{T},\mathscr{R})$       20
$\mathbf{x\ast y}$       243 245
$\mathbf{\Delta_{0}'}$       151
$\mathbf{\Delta_{0}^{+}}$       151
$\mathbf{\Delta_{0}}$       151
$\mathbf{\Delta_{0}}$ formulas      172
$\mathfrak{M}=\mathfrak{M}'\upharpoonright L$       54
$\mathfrak{M}\prec\mathfrak{K}$       82
$\mathfrak{M}\subseteq \mathfrak{K}$       77
$\mathfrak{PR}$       129
$\mathfrak{PR}_{\ast}$       129
$\mathfrak{P}$       128
$\mathfrak{R}$       128
$\mathfrak{R}_{\ast}$       130
$\mathscr{A}(y_{1},...,y_{k})$       18
$\mathscr{A}[y_{1},...,y_{k}]$       18
$\mathscr{R}$ -closed      20
$\mathscr{T(C)}$       76
$\mathscr{T}=\mathscr{T}'\upharpoonright L$       54
$\mu$ -definitions      218
$\mu$ -term      218
$\omega$ -consistent      189
$\omega$ -incompleteness      190
$\omega$ -inconsistent      191
$\omega$ -rule      190
$\overline{i}$       54
$\overline{K}$       145
$\overrightarrow{a}$       19
$\overrightarrow{a}_{n}$       19
$\overrightarrow{x}_{n}$       33
$\pi$ -function      198
$\Pi_{1}$       265
$\Pi_{n}$       151
$\simeq$       126
$\square$       166
$\subseteq$       20
$\sum_{1}$       256
$\sum_{n}$       151
$\tau$ -term      123
$\ulcorner w\urcorner$       155
$\varepsilon$ -term      123
$\varepsilon-\delta$       109
$\{E(x_{1},...,x_{n})\}$       299
${\lim_{x\rightarrow a}}^{\circ}f(x)=b$       108
${\o}$ -index      138
${\o}:\mathfrak{M}\rightarrow_{\prec}\mathfrak{K}$       82
Absolutely provable      37
AC      86
Ackermann function      198
Alphabet      6 13
Alternating chain      96
Ambiguity      24
Ambiguous      24
Antisymmetry      210
Argot      39
Arithmetic      150
Arithmetic hierarchy      151
Arithmetic relations      150
Arithmetical relations      150
Arithmetization      134 265
Arity      8
Ascending chains      93
Assignment function      88
Associativities      17
Automorphism      196
Axiom      6
Axiom, Henkin      65
Axiom, logical      6
Axiom, nonlogical      6 36
Axiom, special      6
Axiomatic theories      38
Axiomatized      38
Axioms, logical      34
Basic diagram      88
Bennett, J.      162
Bernays, P.      41
beta function      159 235
Boolean      7
Boolean operations      133
Bound variable      18
Bounded      112
Bounded multiplication      134
Bounded product      197
Bounded quantification      125
Bounded search      134
Bounded summation      134 197
Bourbaki      5 14 41
Brouwer, L.E.J.      4
C-theory      272
Call by value      144
Cancellation laws      214
Categorical      97
Characteristic function      130 219
Characteristic term      222
Chinese remainder theorem      160
Church's thesis      264
Church, Alonzo      124 188
class      75
Closed form      201
Closed formula      18
Closed interval      111
Closed under      19
Closure      20
Coding      136
Collection      258
Commutative diagram      78
Compact      107
Compactness Theorem      71 74
complete      97 194
Complete arithmetic      39 170
Complete index set      149 199
Complete, simply complete      66

Completeness theorem      52 71 73 194
Completion      195
composition      127
Computability      123
Computable      128
Computable function      124
Computation      140
Computation model      126
Computer program      264
Concatenate      10
Concatenation      13 137 243
Concatenation, formal      243 245
Conjunct      277
Conjunction      17
Conjunctionally      216
Connectives      7
Conservative      115 121 218
Conservative extension      46 118
Consistency theorem      71
Constant      8
Constant, Henkin, Leon      65
Constant, witnessing      65
Construction formative      41
Constructive arithmetic      164 170
Constructive arithmetic predicates      160
continuous      111
Contrapositive      158
Converges      125
Correct      177
Countable      62
Course-of-values induction      214
Course-of-values recursion      137 251
Craig, W.      204
Decision problem      40 188
Decoding      136 240
Dedekind, R.      124 129
Deduced      37
Deduction Theorem      48
Definability      60
Definability in a structure      60
Definable      170 171
Definable in arithmetic      171
Definition by cases      134 221
Definition by positive cases      200
Definition by recursion      25
Derivability conditions      272 296
Derivation      20 254
Derived rule      38
Diagonalization      125 145
Diagonalization lemma      310
Diagram      64 88
Diagram expansion      88
Diagram language      64 88
Diophantine equation      201
Disjunct      276
Distributive laws      193
Diverges      125
Domain      53
Dummy renaming      45
Elementarily equivalent structures      76
Elementary chains      93
Elementary diagram      88
Elementary embedding      82
Elementary extension      82
Elementary substructure      82
Elimination of defined symbols      116 118
Empty sequence      243
Entscheidungsproblem      40 124
Enumeration theorem      153
Equivalence theorem      51 183
Existential axioms      93
Existential formula      113
expansion      88
Explicit definition      218
Explicit transformations      160
Expressions      6
Extension      77
Extensionality      114
Extreme Value Theorem      197
Finitary      4
Finite hyperreal      102
Finitely satisfiable      195
First incompleteness theorem      155
Fixed point      203
fixpoint      203
Fixpoint theorem      310 317
Formal      1
Formal Arithmetic      166 175
Formal language first order      6
Formal, beta function      235
Formalize      3
Formally definable      180
Formally functionally definable      202
Formula form      34
Formula schema      34
Formula, decidable by a theory      66
Formula, mixed-mode      61
Formula, prime      28
Formula, propositional      28
Formula, satisfiable      30
Formula, tautology      30
Formula, unsatisfiable      30
free      18
Free for      32
Free variable      18
Function, computable      128
Function, partial computable      128
Function, partial recursive      128
Function, primitive recursive      129
Function, recursive      128
g-term      296
GCD      157
Generalization      43
Gentzen, Gerhard      193
Goedel number      155
Goedel — Mal'cev compactness theorem      74
Goedel — Rosser first incompleteness theorem      189
Goedel's first incompleteness theorem      177 202
Goedel's second incompleteness theorem      312
Goedel, Kurt      124
Goedel-numbering      155
Graph      98 161 163 199
Greatest common divisor      157
Gries, David      5
Group theory      92
groups      93
Grzegorczyk, A.      132
Halting problem      145
Halting set      145
Henkin theory      66
Henkin, Leon      62 112
Hermes, H.      41
Heyting, A.      4
Hierarchy theorem      154
History function      137
HUbert, D.      4 41
Hyperreal numbers      99
Hyperreals      99
I.H.      22
i.p.      24
identities      128
IFF      11
Immediate predecessors      24
Implied multiplication notation      212
Inclusion map      77
Incompletable      177
Incompletableness      124
Inconsistent      265
Increasing chains      93
Indefinite article      121

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