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| Barwise J., Etchemendy J., Allwein G. — Language, Proof and Logic |
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| Предметный указатель |
singleton set 412 420 440
Skolem function 515
Skolem normal form 515
Skolem paradox 547
Skolem, Thoralf 515
Skolem,Thoralf 546
Skolemization 514 515 521
Smullyan, Raymond 449 555
Sound argument 43 44 140
Sound deductive system 214 214 361
Soundness Theorem for first-order logic 509
Soundness Theorem for propositional logic 215
Soundness Theorem, use of 220
Spatial predicates 401
Step-by-step translation 298 299
Strawson, P.F. 380 381
Strawsonian analysis of definite descriptions 382
Strengthening the antecedent 203 212
Strengthening the consequent 203 212
Structure, first-order 498 495—498 500 506
Structure, truth in 504
submit 5—10
Subproof 149—151 163 206 343
Subproof, end of 164
Subproof, proper use of 163—166
Subset relation 407 412—414
Substitution 49
Substitution of logical equivalents 118 276
Substitution Principle 277
Sufficient condition 179
Summary of game rules 237
Symbolic sciences 2—4
Symmetry 52 422
Symmetry of identity 50
Tarski's World 5—10 14 24
Tarski, Alfred 400 506 556
Taut Con 114—116 158 171 221 272
Taut Con and truth-functional form algorithm 263
Tautological consequence 113 266 469
Tautology 94 97 100 101 103 137 218 219 266 469
Tautology and FO validity 271
Tautology and quantification 257—264
Tautology of fol 262
Tense 398
Terms 32 229
Terms of first-order arithmetic 39
Terms, complex 32 34
Ternary connective 195
Theorem 47 193
Theory, formally complete 472
Theory, formally consistent 471
Transitivity 422
Transitivity of  203 212
Transitivity of < 52
Transitivity of identity 51
Translation 13 28 84
Translation and meaning 84
Translation and mixed quantifiers 289—291 308
Translation and paraphrase 300
Translation of a 231
Translation of all 230
Translation of an 231
Translation of and 71
Translation of any 230 243
Translation of at least n 366
Translation of at least one 231
Translation of at most n 366
Translation of both 379
Translation of but 71
Translation of complex noun phrases 243—244
Translation of conditionals 179
Translation of each 230 243
Translation of every 230 239 243
Translation of everything 228
Translation of exactly n 366
Translation of few 386
Translation of if 179
Translation of if and only if 182
Translation of iff 182
Translation of just in case 182
Translation of many 386
Translation of moreover 71
Translation of most 386
Translation of neither 379
Translation of neither  nor 75
Translation of no 239 243
Translation of non- 68
Translation of not 68
Translation of only if 180
Translation of or 74
Translation of provided 179
Translation of some 231 239
| Translation of something 228
Translation of the 379
Translation of un- 68
Translation of unless 180
Translation, extra exercises 315—318
Translation, step-by-step method 298
Translation, using function symbols 308
Truth 500
Truth assignment 468
Truth conditions 84 84 188
Truth in a structure 504 506
Truth in all worlds 363
Truth table 67
Truth table for 182
Truth table for  68
Truth table for  178
Truth table for  75
Truth table for  72
Truth table, disadvantages of 127
Truth table, joint 106 110
Truth table, method 481
Truth table, modeling in set theory 468—469
Truth table, number of rows 95
Truth table, reference columns 96
Truth value 24 67
Truth, logical 93 94 103 181 182 267
Truth, non-logical 363
Truth, undefinability of 556
Truth-functional form 261
Truth-functional form, algorithm 261—264
Truth-functional, completeness 190 193
Truth-functional, connective 67
Truth-functional, connective, binary 190
Truth-functional, connective, semantics for 68 72 75 178 182
Truth-functional, connective, ternary 195
tt-satisfiable 469
Twin Prime Conjecture 333
Unary function symbol 308
Undefinability of truth 556
Unification 517
Unification algorithm 518
Uninterpreted language 15
union 415 416
Union axiom 435 440
Uniqueness, claim 375
Uniqueness, quantifier,  375
Universal elimination 342
Universal generalization 325 326 332 342
Universal instantiation 321 342
Universal introduction 325 342 343
Universal noun phrase 243 248
Universal quantifier 230
Universal sentence 520
Universal set 432 440
Universal wff 450
Unordered pair 419
Unordered pair, axiom 435
Uses of fol 3—4
Vacuously true generalization 245
Vagueness 21
Valid argument 140
Valid first-order 505
Valid proof 46
Valid step 127 128 319—321
Validity, first-order 266—273
Validity, first-order, and logical truth 271
Variable 228—229
variable assignment 500 506
Variable assignment, appropriate 501
Variable assignment, empty 501
Variable, bound 232 282
Variable, free 231 232
Variable, limited number of 373
Variable, reusing 374
Variable, unbound 231
Vaught, Robert 435
von Neumann, John 434—436 438
Weakening the consequent 203 212
Web address 15
Well-formed formula (wff) 231 231—233
Well-formed formula (wff), atomic 229 231
Well-formed formula (wff), existential 450
Well-formed formula (wff), universal 450
Wellfounded sets 450
Winning strategy for playing the game 78
Witnessing constant 528
Witnessing constant for a wff 529
Witnessing constant, adding to a language 529—530
You try it exercises 7 12
Zermelo — Frankel set theory 435
Zermelo, Ernst 438
ZFC 435 547
| b | 437
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