Classical Mathematical Logic

FrontMatter, pg. i
Contents, pg. vii
Preface, pg. xvii
Acknowledgments, pg. xix
Introduction, pg. xxi
I. Classical Propositional Logic, pg. 1
II. Abstracting and Axiomatizing Classical Propositional Logic, pg. 27
III. The Language of Predicate Logic, pg. 53
IV. The Semantics of Classical Predicate Logic, pg. 69
V. Substitutions and Equivalences, pg. 99
VI. Equality, pg. 113
VII. Examples of Formalization, pg. 121
VIII. Functions, pg. 139
IX. The Abstraction of Models, pg. 153
X. Axiomatizing Classical Predicate Logic, pg. 167
XI. The Number of Objects in the Universe of a Model, pg. 183
XII. Formalizing Group Theory, pg. 191
XIII. Linear Orderings, pg. 207
XIV. Second-Order Classical Predicate Logic, pg. 225
XV. The Natural Numbers, pg. 263
XVI. The Integers and Rationals, pg. 291
XVII. The Real Numbers, pg. 303
XVIII. One-Dimensional Geometry, pg. 331
XIX. Two-Dimensional Euclidean Geometry, pg. 363
XX. Translations within Classical Predicate Logic, pg. 403
XXI. Classical Predicate Logic with Non-Referring Names, pg. 413
XXII. The Liar Paradox, pg. 437
XXIII. On Mathematical Logic and Mathematics, pg. 461
Appendix: The Completeness of Classical Predicate Logic Proved by Gödel's Method, pg. 465
Summary of Formal Systems, pg. 475
Bibliography, pg. 487
Index of Notation, pg. 495
Index, pg. 499