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| Tourlakis G.J. — Lectures in Logic and Set Theory: Mathematical Logic |
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| Предметный указатель |
Indexing theorem 153
Individual variables 7
Induced isomorphism 78
Induction axiom 206
Induction axiom schema 206
Induction hypothesis 22
Induction rule 208
Induction schema 206
Inductive definitions 20
Inductive theories 93
Infinite hyperreal 102
Infinite natural numbers 196
Infinite prime 197
Infinitely close 104
Infinitesimal 97 102
Infix 14 98
Informal 8
Initial functions 128
Input 19
Intermediate Value Theorem 197
Interpretation 53
Iota notation 120
Irreflexive 210
Irreflexivity 210
Iteration theorem 148
Iteratively 21
K 145
Keisler, H. Jerome 88
Kleene normal form theorem 142
Kleene predicate 164
Kleene schemata 127 264
Kleene T-predicate 142
Kleene's Recursion Theorem 149
Kleene, S.C. 124 150
Kronecker, L. 4
Language, extension 54
Language, first order 16
Language, restriction 54
LCM 157
Least common multiple 157 230
Least principle 216
Left endpoint 111
Left field 125
Leibniz rule 51
Leibniz, G.W. 34
lh(x) 240
lh(z) 137 165
Limit ordinal 73
Lindemann, F. 4
Loeb's derivability condition 310
Loeb's theorem 314
Loeb, Martin H. 310 314
Loewenheim — Skolem theorem 71
Logical symbols 7
Logically implies 52
Manin, Yu.I. 39
Markov, A.A. 127
Material implication 17
Mathematical theory see "Theory"
Maximum 230
Metalanguage 3
Metamathematics 3
Metatheory 3
Metavariable 207
modus ponens 36
Monotonicity 50
Monus 131
Mostowski, A. 150
MP 36
Neighbourhood 108
Non-monotone 265
Non-standard hyperreals 99
Non-standard numbers 99
Nontotal 125
Num 296
Num function 296
Number-theoretic functions 124
Numeral 41 171
object variables 7
Occurrence 13
Occurs in 13
One point rule 118
Onto 62
open 92
Open formulas 91
Open theory 91
Operations of substitution 132
Ordered sequence 19
Ordinary computability 124
Ordinary recursion theory 124
Output 19
Pairing function 156
Parsable 29
parse 21
Partial computable 128
Partial function 125
Partial recursive 128
Peano arithmetic 206
Pinching lemma 106
Polynomial 201
Positively strongly definable 191 202
Post's theorem 194
Post, E.L. 124
Predicate 8 130
Prefix 13
Prime power coding 136
Primitive recursion 127
Primitive recursive 129 170 253
Primitive recursive definitions 248
Primitive recursive functions 124 127
Primitive recursive schema 127
Priorities 17
Problem 144
Productive function 179
Productive sets 179
Programming language 264
Projection 128
Projection function symbols 254
Projection functions 156
Projection theorem 147
proof 37
Proof by auxiliary constant 52
Proof by cases 183
Proof by contradiction 50
Proof,  - 37
Proper prefix 13
Proper subtraction 131 222
Propositional axioms 194 269
Propositional calculus 194
Propositional connectives 7
Propositional logic 194
Propositional segment 194
Propositional valuations 29
Propositional variable 28
Provability predicate 280 311
Provably equivalent 42
Proved from 37
Punctured neighbourhood 108
Quine, W.V.O. 156
r.e. predicate 147
Rasiowa, H. 41
Real function 108
Recursion 19
Recursion theorem 149
Recursion theory 123
RECURSIVE 128 130 170
Recursive definition 20
Recursive extension 220 262 265 273
Recursively axiomatizable 39
Recursively axiomatized 38 271
| Recursively enumerable predicate 147
Recursively inseparable 187
Recursively unsolvable 144
Regular 171
Regular formula 171
Regular functions 204
Relation see "Predicate" 8 19
Relation, primitive recursive 130
Relation, recursive 130
Relational notation 125
Relatively prime 157 226
Remainder function 224
Restricted atomic formulas 256
Restriction 78
Rice, H.G. 149
Right endpoint 111
Right finite limit 108
Right positive infinite limit 108
Robinson, Abraham 64
Robinson, R.M. 175
Rosser, J. Barkley 189
Rudimentary functions 174
Rules of Inference 6
Russell's paradox 145
S-m-n theorem 148
Satisfiable 55
Satisfiable, finitely 55
Schema instance 34
Schneider, Fred B. 5
Scope 15
Selection theorem 199
Semi-recursive 170
Semi-recursive index 143
Semi-recursive relations 143
Semigroups 93
Sentence 18
Separation 114
seq 241
Seq(z) 137 165
SEQUENCE 229
Sethood 17
Signum 133
Sikorski, R. 41
Simple completeness 62
Simultaneous substitution 33
Single-valued 86
Skolem function 123
sort 17
Soundness 58
Special Henkin axiom 73
Specialization 43
st(h) 105
Stage 23
Standard hyperreals 99
Standard numbers 99
Standard part 105
String,  13
String,  13
String, empty 13
String, equality 13
String, prefix 13
String, prefix, proper 13
Strong projection theorem 143
Strongly  -recursive 204
Strongly definable 186
Strongly formally definable 186
Strongly term-definable 187
Structure 53
Structure embedding 77
Structure isomorphism 77
Structure, domain of 53
Structure, embedding 77
Structure, expansion of 54 119
Structure, extension of 77
Structure, reduct of 54
Structure, underlying set of 53
Structure, universe of 53
Structures, elementarily equivalent 76
Substitutable for 32
Substitution 31
Substitution function 175 268
Substitution, simultaneous 33
Substring 9 13
Substructure 77
Successor 73 128
Syntactic variable 14 207
T-predicate 142
table 19
Tarski's theorem 174 317
Tarski, Alfred 170 175
Tautology theorem 194
Term, primitive recursive 254
Term-definable 181 252
Term-defined 181
Theorem 36
Theorem schema 40
Theorem, - 36
Theory 38
Theory,  93
Theory, absolute 39
Theory, applied 39
Theory, C 272
Theory, conservative extension of 46
Theory, consistent 38
Theory, contradictory 38
Theory, decides 66
Theory, extension of 46
Theory, first order 38
Theory, Henkin 66
Theory, inconsistent 38
Theory, inductive 93
Theory, open 91
Theory, pure 39
Theory, recursively axiomatized 176
Theory, refutes 66
Theory, semantically complete 62
Theory, simply complete 66
Theory, sound 56
Theory, universal 91
total 98 125
Transfer principle 99
Transfinite sequence 72
Transitive 209
Transitivity of  37
Truth (value) assignment 29
Truth functions 30
Turing Machines 127 264
Turing, Alan 124
Two-sided finite limit 108
TYPE 17
Unambiguous 24
unary 17
Unbounded search 127 216
Uncomputability 124
Undefinability of truth 204
Underlying set 53
union 22
Uniquely readable 29
Universal 265
Universal closure 44
Universal quantifier 17
Universal sentences 94
Universal theory 91
Unsolvable 145
Vacuously satisfied 31
Valid 55
Valid, logically 55
Valid, universally 55
Valuation 29 195
Variable, bound 18
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