Epstein Classical Mathematical Logic

The Semantic Foundations of Logic
Course Book
ISBN: 978-1-4008-4155-4
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 544 Seiten

In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The 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. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations.

The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference.

Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.

Autoren/Hrsg.

Epstein, Richard L.

Weitere Mitwirkende

Szczerba, Leslaw W.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

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

Über Autor(innen)

Richard L. Epstein received his doctorate in mathematics from the University of California, Berkeley. He is the author of eleven books, including two others in the series The Semantic Foundations of Logic (Propositional Logics and Predicate Logic), Five Ways of Saying "Therefore," Critical Thinking, and, with Walter Carnielli, Computability. He is head of the Advanced Reasoning Forum in Socorro, New Mexico.