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| Rautenberg W. — A Concise Introduction to Mathematical Logic (Universitext) |
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| Предметный указатель |
Koenig's lemma 26
Kreisel 199 225
Kripke semantics 221
L-structure (=  -stracture) 35
Language of equations 99
Language, arithmetizable 177
Language, first-order (= elementary) 43
Language, second-order 102
Lattice 39
Lattice of sets 39
Lattice, distributive 39
legitimate 68
Lindstroem's criterion 156
Literal 10 45
Loeb's axiom 221
Loeb's theorem 218
Logic program 122
Logical matrix 40
Logically valid 14 50
Mapping XVI see
Matiyasevich 198
Maximal element 37
Maximally consistent 22 75
Metainduction XIII 183
Metatheory XIII
Model companion 157
Model compatible 150
Model complete 151
Model completion 155
Model interpretable 202
Model of a theory 64
Model, free 110
Model, minimal 117
Model, predicate logical 49
Model, propositional 7
modus ponens 15 29
Monotonicity rule 18
Mostowski 168
n-tuple XVII
Negation 2
Neighbor 25
Nonstandard analysis 85
Nonstandard model 83
Nonstandard number 84
Normal form, canonical 12
Normal form, disjunctive, conjunctive 10
Normal form, prenex 61
Normal form, Skolem 70
Operation XVII
Operation, essentially n-ary 8
Order 37
Order, continuous 37
Order, dense 37 137
Order, linear, partial 37
Ordered pair 89
P-relativised 200
p.r. (= primitive recursive) 169
Pair set 89
Pairing function 172
Parameter definable 85
Paris 219
Partial order 37
Partial order, irreflexive, reflexive 37
Particularization 62
Particularization, anterior, posterior 62
persistent 147
Polish (prefix) notation 6
Power set XVI
Predecessor function 83
Predicate XVII
Predicate, (primitive) recursive 169
Predicate, arithmetical 184
Predicate, Diophantine 184
Predicate, recursively enumerable 175
Preference order 229
Prefix 45
Premise 18
Presburger 159
Prime field 39
Prime formula 4 45
Prime model 133
Prime model, elementary 133
Primitive recursive 169
Principle of Bivalence 2
Principle of extentionality 2
Product, direct 42
Product, reduced 163
Programming language 103
Projection 42
Projection function 169
PROLOG 122
Proof (formal) 29 95
Propositional variables 3
Provable 18 29
Provably recursive 212
Putnam 199
Quantification bounded 171 185
Quantifier 33
Quantifier compression 188
Quantifier elimination 157
Quantifier rank 46
Quasi-identity, quasi-variety 100
Query 122
Quotient field 145
R.e. (recursively enumerable) 174
Rabin 200
RANGE XVI
Rank (of a formula) 6 46
Recursion equations 169
Reduced formula 67 68
Reduct 36 62
Reductio ad absurdum 19
Reflection principle 220
Reflexive 36
Refutable 65
Relation XVI
renaming 60 119
Renaming, bound, free 60
Replacement Theorem 10 59
Representability of functions 187
Representability of predicates 184
Representability Theorem 191
Resolution calculus 113
Resolution closure 113
Resolution rule 113
Resolution Theorem 115
Resolution tree 113
Resolvent 113
Restriction 35
Ring 38
Ring, ordered 39
Rogers 225
Rule 18 72
Rule induction 21 73
Rule of Horn resolution 116
Rule, basic 18 72
Rule, derivable (provable) 18
Rule, Gentzen-style 20
Rule, Hilbert-style 95
Rule, sound 21 72
| S-invariant 145
Sambin 225
Satisfiability relation 14 49
Satisfiable 14 50 65 112
Satisfiably equivalent 69
Scope (of a prefix) 46
Segment XVII
Segment, initial, terminal XVII 37
Semigroup 38
Semigroup, free 38
Semigroup, ordered 38
Semigroup, regular 38
Semilattice 39
Semiring 39
Semiring, ordered 39
Sentence 47
Separator 121
SEQUENCE XVI
Sequent 18
Sequent, initial 18
Set, countable, uncountable 87
Set, densely ordered 137
Set, discretely ordered 142
Set, finite 87
Set, ordered 37
Set, well-ordered 37
Sheffer function 2
Signature, algebraic 45
Signature, extralogical 34
Signature, logical 4
Signum function 170
Singleton 119
Skolem function 69
Skolem's paradox 91
SLD-resolution 126
Solution 123
Soundness 21 73
String XVII
Structure 34
Structure, algebraic, relational 34
Subformula 6 46
Substitution 47
Substitution invariance 99
Substitution theorem 56
Substitution, global 47
Substitution, identical 47
Substitution, propositional 15 16
Substitution, simple 47
Substitution, simultaneous 47
Substring XVII
Substructure 36
Substructure complete 160
Substructure, (finitely) generated 36
Substructure, elementary 133
Subterm 44
Subtheory 64
Successor function 83
Supremum 39
Symbol XVII
symmetric 36
T-model 64
Tarski 16 131 168
Tautologically equivalent 61
Tautology 14 50
Term 44
Term algebra 44 106
Term equivalent 12
Term function 53
Term induction 44
Term model 106
Tertium non datur 14
Theorem, Cantor — Bernstein 135
Theorem, Cantor's 87
Theorem, Dzhaparidze's 227
Theorem, Goodstein's 219
Theorem, Goryachev's 229
Theorem, Herbrand's 108
Theorem, Lagrange's 198
Theorem, Lindenbaum's 22
Theorem, Lindstrom's 101
Theorem, Loewenheim — Skolem 87
Theorem, Los's 164
Theorem, Morley's 139
Theorem, Mostowski's 225
Theorem, Rosser's 195
Theorem, Shelah's 164
Theorem, Solovay's 223
Theorem, Steinitz's 153
Theorem, Trachtenbrot's 98
Theorem, Visser's 224
Theory 64
Theory,  -categorical 137
Theory, (finitely) axiomatizable 81
Theory, arithmetizable 194
Theory, complete 82 137
Theory, consistent (satisfiable) 65
Theory, countable 87
Theory, decidable 93 177
Theory, elementary or first-order 64
Theory, equational 99
Theory, inconsistent 65
Theory, inductive 148
Theory, undecidable 93
Theory, universal 66
Transcendental 38
Transitive 36 229
Truth function 2
Truth table 2
Truth value 2
Truth, true 196
Turing machine 171
U-resolution 126
U-resolvent 125
UH-resolution 126
Ultrafilter 28
Ultrafilter theorem 28
Ultrafilter, nontrivial 28
Ultrapower 164
Ultraproduct 164
Undecidable 81
Undecidable, strongly, hereditarily 197
Unifiable 119
Unification algorithm 119
Unifier 119
Unifier, generic 119
Unit element 38
Universal closure 51
Universal part 145
Universe 89
Urelement 88
Valuation 7 49
Variable 43
Variable, free, bound 46
Variety 99
Vaught 139
Verum 4
w.l.o.g. XVII
Word (over A) XVII
Word semigroup 38
Zorn's lemma 37
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