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| Enderton H.B. — A Mathematical Introduction to Logic |
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| Ïðåäìåòíûé óêàçàòåëü |
Exponentiation, representation of 276—281
Exportation 27
Expressions 15—16 73—74
Extension 95
Extensionality, principle of 2
f 20
Faithful interpretations 171—172
Falsity 20
Field (of relation) 4
Fields 87 92 93—94 285
Fields, real-closed 104
Fields, theory of 155—156 158—159 See
Finite graphs 93
Finite langnage 142
Finite model property 163
Finite models 147—151
Finite sequence (string) 4
Finite set 6
Finitely axiomatizable theories 156
Finitely valid 147
First-order language 67—72 167
First-order language, examples of 70—73
First-order language, formulas 73—76
First-order language, free variables 76—77
First-order language, notation 77—79
First-order logic completeness theorem 135—145
First-order logic deductive calculus 109—129
First-order logic interpretations between theories 164—172
First-order logic language of 69—79
First-order logic models of theories 147—162
First-order logic parsing algorithm 105—108
First-order logic soundness theorem 131—135
First-order logic translation methods 68—69
First-order logic truth and models 80—99
Fischer, Michael 201
Fixed-Point Lemma 234—235
fld R 4
Formal languages 11—13
Formal languages, computer 13
Formal languages, features in 11—13
Formal languages, sentential logic and 13—19
Formula-building operations 17 75
Formulas, atomic 74—75 83
Formulas, comprehension 284
Formulas, generalization of 116
Formulas, satisfaction of 83—86
Formulas, unique readability of 40—41 108
Formulas, well-formed (wffs) 12 17—18 75
Free variables 76—77
Freely generated sets 39—40 See
Frege, Gottlob 152
Function comprehension formulas 284
Function symbols 70 79 128
Function universe 302
Function variables 282
Functions 5
functions, defining 164—166
functions, recursive 247—263
Functions, representable 212—217
Functions, Skolem 145 287—290
gen 122
General pre-structure 301
General second—order logic 303
General structures 299—306
Generalization of formulas 112
Generalization on constants 123—124
Generalization Theorem 117—118
Generated sets 37
Generated sets, freely 39
Goedel, Kurt 145 152
Goedel, Kurt,  -function 278—279 281
Goedel, Kurt, completeness theorem 135—145
Goedel, Kurt, incompleteness theorem 145 236 256 257—258
Goedel, Kurt, numbers 91 184 225—234 286
Goedel, Kurt, second incompleteness theorem 266—270 274—275
Goldbach's conjecture 263
graphs 92
Graphs of function 209
Graphs, connected 146
Graphs, directed 82 93
Graphs, finite 93
groups 38 92
Halting problem unsolvability of 254
Henkin, Leon 145
Herbrand expansions 290—294
Herbrand universe 291
Herbrand's theorem 293
Herbrand, Jacques 293
Heterological 186
Hilbert, David 152
Homomorphism theorem 96—97
Homomorphisms 94—99
Hyperreal numbers See "Nonstandard analysis"
Hypothesis 23 67 109 213
Identity function 5
Identity interpretation 168
Iff, use of 1
Implicant 59
Implicitly definable relations 287
Incompleteness theorem (Goedel), first 145 236 256 257—258
Incompleteness theorem (Goedel), second 266—270 274—275
Incompleteness theorem (Goedel), undecidability and 234—245
Inconsistent sets 119 See
Independent axiomatizations 28
Index of recursive partial function 253
Index of recursively enumerable set 255
Individual variables 282—283
Induction 30 34—38
Induction axiom See "Peano induction postulate"
Induction principle 18—19 37 44 111—112
Inductive sets 35
Infinitely close 177
Infinitesimal 176
Initial segment 4
Input/output format 62 209
Instances 291
Integers 2
Interpolation theorem 53
Interpretations 80
Interpretations between theories 164—172 273
Intersection 3
IR 261
Isomorphic embedding 94
Isomorphic structures 94
Isomorphism 94
K 254
Kleene normal form 249—250 252—254 257
Kleene's theorem 64 239
Lagrange's theorem 166
Languages of equality 285 See "Formal "Second-order
Languages, many-sorted 299—301
Least-zero operator 216 220—221
Leibniz, G.W. v. 173
Length 221
lh 221
Lindenbaum's theorem 246
Linear connectives 52
Linear transformations 99
Literal 59
ln 194
Loeb's theorem 269
Loewenheim — Skolem theorem 103 151—155 190
Loewenheim — Skolem theorem in many-sorted logic 299
Loewenheim — Skolem theorem in second-order logic 285 302—303
Loewenheim, Leopold 151
Logical axioms 110 112 125
Logical axioms, recursiveness of 232
Logical axioms, validity of 131—134
Logical implication 88—99
Logical symbols 14 69—70
| Logically equivalence 88
Los-Vaught test 157—160 190
LST theorem 154
Lukasiewicz, Jan 33 See
Majority connective 45
Malcev, Anatolii 145
Many-one reducibility 256
Many-sorted logic 295—299
Many-sorted logic, application to second-order logic 299—301
Many-valued logic 20
MAP 5
Map coloring 65 146
Material conditional 21
Membership predicate 299—300
meta-language 89 129
Metamathematics, use of term 69
Metatheorems 116—120
MN 203
MOD 92
Models 80—99
Models of analysis 304—306
Models of theories 147—162
modus ponens 66 110—111 116
Monotone connectives 54
Monotone recursion 224
MP 122
NAND 51
Natural numbers 2 See
Negation symbol 14 17
Newton, Isaac 173
Nonlogical symbols 14
Nonprime formulas 114
Nonstandard analysis 173—181
Nonstandard analysis, algebraic properties 176—178
Nonstandard analysis, construction of hyperreals 173—176
Nonstandard analysis, convergence in 178—180
Nonstandard models 152—153 183 304
Normal form theorem, for recursive functions 252—253
Normal form theorem, Skolem 288—289
Notation 77—79
NP 26 101
Number theory 182
Number theory, language of 70 72 182
Number theory, with addition 196—197 280
Number theory, with exponentiation 202—205 280
Number theory, with multiplication 276—281
Number theory, with ordering 193—196 280
Number theory, with successor 187—193 280
Numerals 183—184 209
Numeralwise determined formulas 206 210—212
Object language 89
Occur free 76—77
One-sorted logic 296—299
One-to-one functions 5
Onto 5
Operating System 253
Operations 5
Ordered n-tuples 3—4
Ordered pairs 3 4
Ordering relations 6 93 159 284
PA 269
Pairing function 220 277—278
Pairwise disjoint set 3
Parameter Theorem 258—260 264
Parameters 14 70
Parentheses, use of 33 78
Parity connective 53
Parsing algorithm in first-order logic 105—108
Parsing algorithm in sentential logic 29—33
Parsing formulas 29—33 107—108
Parsing terms 106—107
Partial functions 250
Partial recursive functions See "Recursive functions partial"
Partition 6
Peano arithmetic (PA) 269—270
Peano induction postulate 193 284 286—287
Periodic set 201
Permutation 100
Polish notation 32—33 74
Polynomial-time decidable 26 115
Post, Emil 47 152 261
Power set 2—3
Prb 266
Predicate calculus See "First-order logic"
Predicate symbols 70 79 128
Predicate variables 282
Prenex formulas 160
Prenex normal form 160—161
Prepositional logic 14
Presburger's theorem 197—198
Prime formulas 114—115
Prime implicants 59
Prime numbers 91 184 218—219
Primitive recursion 221—222 227
Principia Mathematica (Whitehead and Russell) 152
Proof, nature of 109 See
Proposition symbol 14—15
Psb 232
Qn 121 160
Quantifier capture 113
Quantifier symbol, universal 80
Quantifiers 70
Quantifiers, bounded 204 210—211
Quantifiers, elimination of 190—192
Quantifiers, existential 287 288
Quotient structure 140
RAA 122
Rabin, Michael 201
Ramified analytical sets 306
ran R 4
Range (of relation) 4
Re-replacement lemma 130
Reasonable language 142—144 See
Recursion 32 38—4
Recursion theorem 39—42
Recursion, monotone 224
Recursion, primitive 221—222 227
recursive functions 247—250
Recursive functions, normal form 248—250
Recursive functions, partial 250—258 262
Recursive functions, reduction of decision problems 258—260
Recursive functions, register machines 261—263
Recursive relations 207—210 232 See
Recursively axiomatizable theories 233 240
Recursively enumerable (r.e.) relations 233 238—241
Recursively inseparable sets 245
Recursively numbered language 225
Reductio ad absurdum 119 121
Reducts of number theory 182—183 193—202
Reflexive relations 5
Register machines 208 261—263
Relation comprehension formulas 284
Relation universe 301
Relations 4—6
Relay circuits 57
Representable functions 212—217
Representable relations 205—206
Representable relations and numeralwise determined formulas 206 210—212
Representable relations, weakly 241—242
Resolution 53
Restriction 5 221
Rice's theorem 260
Rigid structure 98
Robinson, Abraham 173
Root of tree 7
Rule EI 124—125 145
Rule T 118
Rules of Inference 110
s(x | d) 84
S-m-n theorem See "Parameter theorem"
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