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| Ebbinghaus H., Flum J., Thomas W. — Mathematical Logic: Undergraduate Texts in Mathematics (Undergraduate texts in mathematics) |
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| Предметный указатель |
 -function lemma 169
 -elementary class 92
Accessible 207
Add-instruction 151
Algol 155
Algorithm 146
Alphabet 10
Alphabet of a first-order language 13
AND 13
Antecedent 59
Aristotle 3
Arithmetic 27 96
Arithmetic, Peano 165
Arithmetic, undecidability of 168
Arithmetical relation 172
ASSIGNMENT 27 132
Automorphism 40
Axiomatizable 166
Axioms, system of 7
Back-property 182
Barwise compactness theorem 139
Bolzano 35
Boole 3
Bound occurrence 23
Calculus 14 17
Calculus, induction over a 18
Calculus, rule of a 17
Calculus, sequent 59
Church 154 162
Church's thesis 155
Class of models 91
Class of models, -elementary 92
Class of models, elementary 92
Classical mathematics 103
Coincidence lemma 35
Compactness Theorem 90 134 138 143 195
Complete theory 166
Completeness theorem 87 135
Computable function 149 154
Configuration 160
Conjunction 15
Conjunctive normal form 127
Connective 8 28
Consequence relation 5 8 32
Consistency of mathematics 177
Consistency of ZFC 177
Consistent 72
Consistent, maximally 77
Constant 13
Containing witnesses 72
Continuum Hypothesis 110
Correct rule 59
Correct sequent 59
Correctness of  , theorem on 70
Countable 1
Countable, at most 11
Decidable 146 154
Decision procedure 146
Dedekind's Theorem 47 104
Definition by induction on formulas 21
Definition by induction on terms 21
Definition in a set of sentences 116
Definitions, theorem on 118
Dense ordering 183
Derivable 59 69
Derivable rule 61
Derivation 14
Descending chain 98
Direct product 40
Disjunction 15
Disjunctive normal form 126
Domain 27
Effective procedure 146
Ehrenfeucht game 191
Elementarily equivalent 194
Elementary class 92
Enumerable 147 157
Enumeration procedure 147
Equality symbol 13
Equivalence relation 5
Equivalence structure 6
Equivalence, axioms for 5
expansion 37
Extensional 29
Field 44 92
Field, Archimedean 96
Field, ordered 44
Fin-satisfiable 162
Fin-valid 162
Finite structure 93 162
Finitely axiomatizable 166
Finitely isomorphic 182
First-order language 15
First-order object 9
First-order, alphabet of a 13
Fixed point theorem 174
Follows from 5 7 8
For all 13
Formally provable 59 69
Formula 7 15
Formula in Polish notation 23
Formula, atomic 15
Formula, Horn 41
Forth-property 182
FORTRAN 155
Fraisse's theorem 185
Free occurrence 23
Frege 3 17
Function 26
Function, partial 45
Goedel 87
Goedel completeness theorem 8 87
Goedel number 156
Goedel numbering 156
Goedel's first incompleteness theorem 176
Goedel's second incompleteness theorem 177
Group 4
Group theory 4
Group theory, axioms of 4
Group, torsion 46 93
Halt-instruction 151
Halting problem 156
Henkin 78
Henkin's theorem 79
Herbrand's theorem 84
hilbert 3
Hilbert's program 3 112 177
Idemitas indiscernibilium 133
If and only if 13
If-then 13
Implication 15
Incompleteness of second-order logic 164
Inconsistent 72
Independent set of sentences 41 94
Induction over a calculus 18
Inductive definition on terms or formulas 21
Infinitary language 137
Instruction 14
Intensional 29
Interpretation 27
Intuitionism 103
Isomorphic 38
Isomorphic, finitely 182
Isomorphic, partially 182
Isomorphism 38
Isomorphism lemma 38
Isomorphism, partial 180
Label 151
Language, first-order 9 15
Language, formal 7
| Language, many-sorted 45
Language, object 17
Language, second-order 9 132
Law of the excluded middle 62
Leibniz 3 87 162
Length of a string 10
Liar's paradox 173
Lindstroem 193
Lindstroem's First Theorem 199
Lindstroem's Second Theorem 204
Llull 87 162
Loewenheim — Skolem theorem 88 134 139 175
Loewenheim — Skolem theorem, downward 89
Loewenheim — Skolem Theorem, Upward 90
Loewenheim — Skolem — Tarski Theorem 91
Logic, mathematical 1
Logical system 193
Logical system effective 203
Logical system effectively regular 203
Logical system regular 195
Logically equivalent 33
Matrix 126
Metalanguage 17
Model 31 37
Model theory 98
modus ponens 63
Negation 15
Nonstandard analysis 98
Nonstandard model of arithmetic 96
NOT 13
Object, first-order 9
Object, second-order 9
OR 13 29
Ordering 43
Ordering, partially defined 43
PARAMETER 23
Partial isomorphism 180
Partially isomorphic 182
Peano 17
Peano arithmetic 165
Peano axiom system 47
Peano structure 104
Philosophy 3
Predicate calculus, first-order 15
Prefix 126
Prenex normal form 126
Print-instruction 151
Proof by induction on formulas 19
Proof by induction on terms 19
Proof by induction over a calculus 18
Proof, formal 8 101
Proposition 7
Propositional calculus 30 87
Quantifier 8
Quantifier number 127
Quantifier rank 187
Quantifier, for all 13
Quantifier, there are uncountably many 142
Quantifier, there exists 13
Quantifier-free 126
R-axiomatizable 166
Rank 55
RECURSIVE 155
Recursively enumerable 155
Reduct 37
register 150
Register machine 150
Register program 151
Register-computable (R-computable) 154
Register-decidable (R-decidable) 154
Register-enumerable (R-enumerable) 154
Regular logical system 195
Relation 26
Relation, arithmetical 172
Relation, representable 172
Relation, symbol 13
Relational symbol set 120
Relativization 123
Relativization lemma 123
Representable function 172
Representable relation 172
Rule 8 14 17
Rule, connective 60
Rule, derivable 61
Rule, equality 65
Rule, quantifier 65
Rule, structural 60
Russell 3 87
S-closed 122
Satisfaction relation 31
Satisfiable 33 195
Second-order logic 132 164
Second-order object 9
Self-referential 174
Semantic 26
Sentence 24
Sentence of  193
Sequent 59
Sequent calculus 59 142
Sequent calculus, theorem on the adequacy of the 87
Set theory, background 107
Set theory, object 108
Set theory, system of axioms for 105
Set theory, ZFC axioms for 108
Simple group 141
Skolem's paradox 108 112
Skolem's theorem 96
Spectrum 44
String 10
String, empty 10
Structure 26
Structure, many-sorted 45
Substitution lemma 52
Substitution, simultaneous 49
Subtract-instruction 151
Succedent 59
Symbol set 13
Symbol, "logical" 13
Symbol, equality 13
Symbol, function 13
Symbol, relation 13
Syntactic 26
Tarski 35
Tarski's theorem 175
Term 14
Term interpretation 79
Term reduced 121
Term structure 79
Tertium non datur 62
Theorem on the adequacy of the sequent calculus 87
Theorem on the correctness of the sequent calculus 70
Theory 165
Theory of a structure 94
There exists 13
Trahtenbrot's theorem 163
Truth-value 29
Uncountable 11
Undecidability of arithmetic 168
Undecidability of first-order logic 159
Undecidability of the halting problem 156
Universe 27
Universe, mathematical 104
Urelement 105
Valid 33 195
Variable 13
Variables, set of free 23
Vector space 45 94
Weak second-order logic 136 164
Well-ordering number 207
Whitehead 87
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