Enderton H.B. — A Mathematical Introduction to Logic :: Электронная библиотека попечительского совета мехмата МГУ

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Enderton H.B. — A Mathematical Introduction to Logic

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Название: A Mathematical Introduction to Logic

Автор: Enderton H.B.

Аннотация:

In his textbook for an advanced undergraduate introductory mathematics course in logic ranging from a quarter to a year, Enderton (U. of California-Los Angeles) discusses proofs, truth, and computability for students with some mathematical background and interests but have not studied logic before. He intends the second edition to be more accessible to typical undergraduate students, more flexible for instructors, and more focused on the influence of theoretical computer science on logic. He mentions no date for the first edition.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2001

Количество страниц: 317

Добавлена в каталог: 29.11.2009

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Предметный указатель

#      45
$(a)_{b}$       220
$A \times B$       4
$a\ast b$       222
$A\thicksim B$       8
$a\upharpoonright b$       221
$A^{n}$       4
$A_{E}$       202
$A_{l}$       194
$A_{M}$       276
$A_{ST}$       161
$A_{s}$       188
$A_{ZF}$       157
$B^{n}_{\alpha}$       46
$c^{*}$       35
$C_{*}$       35
$EC_{\triangle}$       92
$E_{n}$       300
$f \circ g$       5 180
$f:A\rightarrow B$       5
$F^{n}_{i}$       282
$K_{R}$       217
$p_{n}$       219
$Q_{i}$       297
$s^{\mathfrak{A}}$       81
$t_{m}$       249
$W_{e}$       255
$X^{n}_{i}$       282
$[[e]]_{m}$       252
$\aleph_{0}$       9
$\alpha^{x}_{t}$       112
$\ast$       223
$\bigvee_{i}$       200
$\bigwedge$       110
$\bigwedge_{i}$       195
$\cap$       3
$\cup$       3
$\dashv$       1
$\downarrow$       51
$\equiv_{n}$       197
$\exists!$       102
$\exists$       68 77 226
$\exists_{n}$       102
$\forall$       68 226
$\forall_{n}$       102
$\in$       1
$\intercal$       50
$\lambda_{n}$       147
$\langle a_{0},...,a_{n}\rangle$       220
$\langle x_{1},...,x_{n}\rangle$       3 4
$\langle \mathsf{R} \rangle$       305
$\Leftarrow$       1
$\leftrightarrow$       1
$\leq$       194
$\leq_{m}$       256
$\mathbb{D}\mathcal{A}$       305
$\mathbb{N}$       2
$\mathbb{Q}$       87
$\mathbb{R}$       5
$\mathbb{Z}$       2
$\mathcal F_f$       74
$\mathcal{D}$       32
$\mathcal{E}$       17
$\mathcal{F}$       175
$\mathcal{G}$       184 226
$\mathcal{I}$       176
$\mathcal{P}$       2
$\mathcal{Q}_{i}$       75
$\mathfrak{A}\cong\mathfrak{B}$       94
$\mathfrak{A}\equiv\mathfrak{B}$       97
$\mathfrak{A}^{\ast}$       297
$\mathfrak{B}^{\sharp}$       297
$\mathfrak{R}$       182 183
$\mathrm{E}$       71 182
$\mathrm{l}^{m}_{i}$       214
$\mathrm{S}$       71 182
$\mathrm{T}$       118 122
$\mid$       51
$\mid\mathfrak{A}\mid$       81
$\models$       23 88
$\models=\mid$       24 88
$\mu b_{-}$       216 221
$\mu$ -operator      216 220—221
$\natural$       230
$\neg$       11
$\neq$       77 78
$\nleq$       194
$\nless$       78
$\notin$       1
$\nu_{n}$       68
$\nvDash$       1
$\omega$ -completeness      223
$\omega$ -consistency      241 245
$\omega$ -models of analysis      304—306
$\overline{f}$       221
$\overline{h}$       38
$\overline{s}$       83
$\overline{V}$       20
$\perp$       50
$\Phi$       297
$\pi^{-1}[T]$       168
$\pi_{s}$       167
$\pi_{\mathfrak{B}}$       168
$\preceq$       8
$\prod_{n}$       242
$\rho$       258
$\rightarrow$       1
$\sharp\varphi$       184 225
$\sigma_{n}$       242
$\simeq$       177
$\star$       62
$\subseteq$       2
$\succ^{k}\mathrm{u}$       183
$\therefore$       1
$\triangle_{n}$       243
$\underline{\cdot}$       262
$\varepsilon_{n}$       299
$\varphi(t_{1},...,t_{n})$       167 204
$\varphi^{\pi}$       169
$\vDash _{\mathfrak{A}} \varphi[s]$       83
$\vDash$       110
$\vDash\mathfrak{A}\varphi[[a_{1},...,a_{n}]]$       86
$\vDash^{G}_{\mathfrak{A}} \varphi[s]$       302
$\vee$       12
$\wedge$       11
$\{x_{1},...,x_{n}\}$       2
${\O}$       2
*A      175
+      51 71 82
.      71 182
0      70 182
0-ary connectives      50
0-place function symbols      70
<      70 182
=      1 68 69
A;t      2
abbreviations      1
Absolute model      304 305
Absolute second—order logic      303
Adjoining      2
Algebraic numbers      10
Algebraically closed fields      158—159
Algorithm      61
Alphabetic variants      126—127
AN      203
Analysis, models of      304—306
Analysis, nonstandard      See "Nonstandard analysis"
Arithmetic      See "Number theory"
Arithmetical hierarchy      242—245
Arithmetical relations      100 242

Arithmetization of syntax      224—234
Asser, Guenter      101
Atomic formulas      74—75 83
Automorphism      98—99
Ax      122
Axiomatizable theory      156—157
Axioms, logical      See "Logical axioms"
Berkeley, George      173
Biconditional symbol      14
Binary connectives      51
Bolzano — Weierstrass theorem      181
Boolean algebra      20
Boolean functions      45—52
Bound variables      80
Bounded quantifiers      204 210—211
Bridge circuit      57
C++      13
Calculus, deductive      See "Deductive calculus"
Cantor's theorem      159 163
Cantor, Georg      8
Capital asterisk operation      223
card A      8
Cardinal arithmetic theorem      9—10
Cardinal numbers      8—10
Cardinality of languages      141
Cardinality of structures      153—154 157
Carroll, Lewis      162
Cartesian product      4
Categorical sets      154 157
Categoricity in power      157
Chain      7
Chain rule      180
Characteristic function      217
Chinese remainder theorem      91 279
Church's Theorem      145 164 238
Church's thesis      185 187 206—210 233—234 240 247
Circuits, switching      54—59
Closed      5 18 35 111
CN      155
Compactness theorem history of      145
Compactness theorem in first-order logic      109 142 293
Compactness theorem in many-sorted logic      298
Compactness theorem in second-order logic      285 303
Compactness theorem in sentential logic      24 59—60
Complete sets of connectives      49
Complete theory      156
Completeness theorem      66 135—145
composition      5 215—216
Comprehension formulas      284
Computability approach to incompleteness      184 187 257—258
Computable      65 208—209
Computable functions      209—210 250—251 See
Computably enumerable(c.e.)      238
Computing agents, idealized      208 261—263
Concatenation function      222—223
Conditional sentence      21
Conditional symbol      14
Congruence relation      140
Conjunction symbol      14
Conjunctive normal form (CNF)      53
Connectives      See "Sentential connectives"
Cons      67
Consequences, set of      155
Consequent      113
Consistent sets      119 135
Constant symbols      70 79
Constants, generalization on      123—124
Construction sequences      17—18 35—37 111
Contraposition      27 119 121
Convergence      178—180
Countable language      135 145 151—153
Countable sets      6
Craig's Theorem      163
D'Alembert, Jean      173
De Morgan's laws      27 49
Decidable sets      62—63 144 185 See
Decidable theory      144 157 See
Decoding function      220
ded      122
Deducible formulas      111
Deduction Theorem      118—120
Deductions      66 110—112
Deductive calculus      66 109
Deductive calculus, alphabetic variants      126—127
Deductive calculus, equality      127—128
Deductive calculus, formal deductions      110—112
Deductive calculus, metatheorems and      116—120
Deductive calculus, strategy      120—126
Deductive calculus, substitution      112—114
Deductive calculus, tautologies      114—116
Definability in a structure      90—92
Definability of a class of structures      92—94
Definable element      91
Definable relations      90—92 98 287
Definable relations from points      103
Defined function symbols      164—166 169 172
Definition by recursion      38—44
Delay of circuit      56
Dense order      159
Depth of circuit      56
Derivability conditions      267
Descriptions      See "Defined function symbols"
Diagonal function      264
Diagonalization approach to incompleteness      184 186—187 245—246
Directed graphs (digraphs)      82 93
Disjoint set      3
Disjunction symbol      14
Disjunctive normal form (DNF)      49
Divisibility      218
dom R      4
Domain of relation      4
Domain of structure      81
Dominance      8—9
Donkey sentences      80
Double Negation      89
Dovetailing      64
Dr      261
Duality      28
EC      92
Effective computability      65 See
Effective enumerability      63—66 See
Effective procedures      61—65 See
EI      124
Elementarily closed (ECL)      104
Elementary class ( $EC, EC_{\triangle}$ )      92—93
Elementary equivalence      97
Elementary substructure      294
Elementary type      104
Eliminable definition      172
Elimination of quantifiers      190—192
EN      203
Entscheidungsproblem      164
Enumerability theorem      109 142—143 145 293
Enumerability theorem in many-sorted logic      298
Enumerability theorem in second-order logic      286 303
EQN      122 127
Equality      1—2 127—128
Equality symbol      70
Equality, language of      246 285
Equinumerous      8
Equivalence classes and relations      6 189
Euler, Leonhard      5 173
Evaluation function parameter      300
Eventually periodic set      201
Excluded Middle      27
Exclusive disjunction      51
Existential formula ( $\exists_{1}$ )      102 205
Existential instantiation (rule EI)      124—125 145
Existential quantifiers      67 87 287 288
Exponential growth      26

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