Description
Book SynopsisRelates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. This book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings.
Trade Review"[Richard Epstein] never gives only the technical side of the matter, but...always offers intuitive motivations and explains basic decisions which constitute the whole approach, and which build a bridge to the students' experiences, with natural language as well as with standard 'elementary' mathematics. The book is a self-contained textbook, requiring as background only some facility in mathematics...This makes the book particularly suitable as a textbook for self-study."--Siegfried J. Gottwald, Zentralblatt MATH
Table of Contents*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 Godel's Method, pg. 465*Summary of Formal Systems, pg. 475*Bibliography, pg. 487*Index of Notation, pg. 495*Index, pg. 499
