Rautenberg W. — A Concise Introduction to Mathematical Logic (Universitext) :: Электронная библиотека попечительского совета мехмата МГУ

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Rautenberg W. — A Concise Introduction to Mathematical Logic (Universitext)

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Название: A Concise Introduction to Mathematical Logic (Universitext)

Автор: Rautenberg W.

Аннотация:

This is the best introductory text in logic available. It only lacks a coverage of set theory, and I advise the author to include it as chapter 4 of the third edition.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-е издание

Год издания: 2006

Количество страниц: 273

Добавлена в каталог: 06.08.2014

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Предметный указатель

$\beta$ -function      189
$\Delta$ -elementary class      139
$\delta$ -function      170
$\Delta_{0}$ -formula      185
$\Delta_{0}$ -induction      206
$\exists$ -formula      54
$\exists$ -formula, simple      158
$\forall \exists$ -sentence, $\forall \exists$ -theory      148
$\forall$ -formula, $\forall$ -sentence      54
$\forall$ -theory      66
$\mathbb{Z}$ -group      159
$\mathcal{L}$ -formula      46
$\mathcal{L}$ -model      49
$\mu$ -operation      169
$\mu$ -operation, bounded      172
$\omega$ -consistent      195
$\omega$ -incomplete      196
$\omega$ -rule      226
$\omega$ -term      90
$\phi$ -maximal      32
$\prod_{1}$ -formula      184
$\Sigma_{1}$ -completeness      186
$\Sigma_{1}$ -completeness, provable      215
$\Sigma_{1}$ -formula      184
$\Sigma_{1}$ -formula, special      208
(finitely) generated      36
(Monic) polynomial      82
(Recursively) decidable      169
(Relatively) interpretable      200
<-induction      86
A.c. (algebraically closed)      38
Abelian group      38
Abelian group, divisible      81
Abelian group, torsion-free      82
Abraham Robinson      85
Absorption laws      39
Algebra      34
algebraic      38
Almost all      48 163
Alphabet      XVII
antisymmetric      36
Arithmetical      184
Arithmetical hierarchy      205
Artin      147
Associative      37
Automated theorem proving      94
Automorphism      40
Axiom of Choice      90
Axiom of continuity      85
Axiom of extensionality      88
Axiom of foundation      90
Axiom of infinity      90
Axiom of Power Set      89
Axiom of replacement      89
Axiom of union      89
Axiom system of a theory      65
Axiom system, logical      29 95
Axiomatizable      81
Axiomatizable, finitely, recursively      81
Basis theorem for formulas      160
Basis theorem for sentences      140
Behmann      98
Birkhoff rules      99
Boolean algebra      39
Boolean algebra of sets      39
Boolean algebra, atomless      156
Boolean basis for $\mathcal{L}$ in T      160
Boolean basis for $\mathcal{L}^{0}$ in T      140
Boolean combination      45
Boolean function      2
Boolean function, dual, self-dual      12
Boolean function, linear      8
Boolean function, monotonic      13
Boolean matrix      40
Boolean signature      4
cardinal number      134
Cardinality      134
Cardinality of a structure      135
Chain      37
Chain of structures      148
Chain of theories      80
Chain, elementary      148
Characteristic      39
Church's thesis      171
Clause      112 118
Clause, definite, positive, negative      112
Closed under MP      30
Closure axioms      200
Closure of a formula      51
Closure of a model in T      152
Closure, deductive      16
Cofinite      28
Collision of variables      55
Collision-free      56
Commutative      37
Compactness Theorem      24 82
Compatible      65
Completeness theorem      80 96 97
Completeness theorem, Birkhoff's      100
Completeness theorem, propositional      23
Completion      93
Completion, inductive      150
composition      XVI 169
Computable      169
Concatenation      XVII
Concatenation, arithmetical      174
Congruence      41
Congruence classes      41
Congruence in $\mathcal{L}$       58
Conjunction      2
Connective      3
Connex      36
Consequence relation      16 17
Consequence relation, finitary      16
Consequence relation, local, global      63
Consequence relation, predicate logical      51
Consequence relation, propositional      15
Consistency extension      220
Consistent      75 123
Constant      XVII
Constant expansion      76
Constant-quantihcation      76
Continuity Schema      86
Continuum Hypothesis      135
Contradiction      14
Contraposition      17
Converse implication      3
Coprime      185
Course-of-values recursion      174
Cut rule      20
Davis      199
Decidable      81
Deduction Theorem      17 31
Deductively closed      16 64
Definable      53
Definable in a structure      53
Definable in theories      211
Definable with parameters      85
Definable, explicitly      53 69
Definable, implicitly      69
DeJongh      225
Derivability conditions      210
Derivable      18 19 29
Diagram      132
Diagram, elementary      133
Diagram, universal      149
Direct power      42
Disjunction      2
Disjunction, exclusive      2
Distributive laws      39

Domain      XVI 34
Ehrenfeucht game      142
Elementary class      139
Elementary equivalent      55
Elementary type      139
Embedding      40
Embedding, elementary      136
End extension      84 186
Enumerable, effectively or recursively      92 174
equation      45
Equation, Diophantine      184 198
Equipotent      87
EQUIVALENCE      3
Equivalence class      41
Equivalence relation      36
Equivalent      9 50
Equivalent in (or modulo) T      65
Equivalent in a structure      59
Equivalent, logically or semantically      9 50
Euclid's lemma      189
Existentially (or $\exists$ -)closed      149
Existentially closed      155
expansion      36 62
Explicit definition      68
Extension      36 64
Extension of a language      62
Extension of a theory      64
Extension, conservative      52 67
Extension, definitorial      68
Extension, elementary      133
Extension, finite      65
Extension, immediate      152
Extension, transcendental      138
f-closed      35
Factor structure      41
Falsum      4
Family (of sets)      XVI
Fermat's conjecture      199
Fibonacci sequence      174
Fictional argument      8
Field      38
Field of algebraic numbers      134
Field of characteristic 0 or p      39
Field, algebraically closed      38
Field, ordered      39
Field, real closed      153
Filter      27
Filter, proper, principal      28
Finitary      16
Finite model property      97
Finiteness theorem      21 23 73 81
Fixed-Point Lemma      194
Formula      45
Formula algebra      34
Formula induction      5 46
Formula, Boolean      4
Formula, closed      47
Formula, defining      67
Formula, dual      12
Formula, first-order      45
Formula, open (quantifier-free)      45
Formula, prenex      61
Formula, representing      8 184
Formula, universal      54
Four-colour Theorem      26
Frege      60
Function      XVI
Function, bijective      XVI
Function, characteristic      169
Function, identical      XVI
Function, injective, surjective      XVI
Function, partial      138
Function, primitive recursive      169
Function, recursive (= $\mu$ -recursive)      169
Functional complete      12
Gap      37
Generalization      62
Generalization, anteriour, posterior      62
Generalized of a formula      51
Generally valid      50
Gentzen calculus      18
Goal clause      123
Goedel number      173
Goedel number of a number sequence      173
Goedel number of a proof      177
Goedel number of a string      176
Goedel term      191
Graph      37
Graph of an operation      XVII
Graph, k-colorable      25
Graph, planar, simple      25
Ground (or constant) term      44
Ground instance      107
Group      38
Group, ordered      38
Groupoid      38
H-resolution      116
Harrington      219
Henkin set      77
Herbrand model      108
Herbrand model, minimal      111
Herbrand universe      108
Hilbert calculus      29 95
Homomorphism      40
Homomorphism theorem      41
Homomorphism, canonical      41
Homomorphism, strong      40
Horn clause      116
Horn formula      109
Horn formula, basic      109
Horn formula, positive, negative      109
Horn formula, universal      109
Horn resolution      117
Horn sentence      109
Horn theory      109
Horn theory, universal, nontrivial      110
Hyperexponentiation      186
I-tuple      XVI
Idempotent      37
Identity      99
Immediate predecessor      37
Immediate successor      37
Implication      3
Incompleteness Theorem, First      194
Incompleteness Theorem, Second      217
Inconsistent      22 75
Independent (of T)      65
Individual variables      43
Induction axiom      84
Induction hypothesis      83
Induction on $\phi$       7 46
Induction on t      44
Induction schema      83
Induction step      83
Infimum      39
Infinitesimal      86
Instance      107 123
Integral domain      38
Interpretation      49
Invariance Theorem      55
Invertible      37
Irreflexive      36
Isomorphism      40
Isomorphism, partial      138
j-term      68
Jeroslow      225
Julia Robinson      199
Jump      37
Kernel (of a prenex formula)      61
Kleene      169 205

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