Logical Labyrinths

vi
Contents
III Infinity 133
14 The Nature of Infinity 135
15 Mathematical Induction 157
16 Generalized Induction, König’s Lemma, Compactness 173
IV Fundamental Results in First-Order Logic 189
17 Fundamental Results in Propositional Logic 191
18 First-Order Logic: Completeness, Compactness,
Skolem-Löwenheim Theorem 205
19 The Regularity Theorem 217
V Axiom Systems 227
20 Beginning Axiomatics 229
21 More Propositional Axiomatics 245
22 Axiom Systems for First-Order Logic 267
VI More on First-Order Logic 275
23 Craig’s Interpolation Lemma 277
24 Robinson’s Theorem 285
25 Beth’s Definability Theorem 291
26 A Unification 297
27 Looking Ahead 309
References 321
Index 323