Classical Mathematical Logic

The Semantic Foundations of Logic

Richard L. Epstein

522 pages, parution le 27/06/2006

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Résumé

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.

L'auteur - Richard L. Epstein

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.

Sommaire

Preface
Acknowledgments
Introduction
Classical Propositional Logic
Abstracting and Axiomatizing Classical Propositional Logic
The Language of Predicate Logic
The Semantics of Classical Predicate Logic
Substitutions and Equivalences
Equality
Examples of Formalization
Functions
The Abstraction of Models
Axiomatizing Classical Predicate Logic
The Number of Objects in the Universe of a Model
Formalizing Group Theory
Linear Orderings
Second-Order Classical Predicate Logic
The Natural Numbers
The Integers and Rationals
The Real Numbers
One-Dimensional Geometry
Two-Dimensional Euclidean Geometry
Translations within Classical Predicate Logic
Classical Predicate Logic Logic with Non-Referring Names
The Liar Paradox
On Mathematical Logic and Mathematics
Appendix: The Completeness of Classical Predicate Logic Proved by Gödel's Method
Summary of Formal Systems
Bibliography
Index of Notation
Index

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	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Richard L. Epstein
Parution	27/06/2006
Nb. de pages	522
Format	18 x 26
Couverture	Relié
Poids	1111g
Intérieur	Noir et Blanc
EAN13	9780691123004
ISBN13	978-0-691-12300-4