Classical Mathematical Logic The Semantic Foundations of Logic 1st Edition by Richard L Epstein,Leslaw W Szczerba ISBN 0691123004 978-0691123004

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Product details:

ISBN 10: 0691123004 

ISBN 13: 978-0691123004

Author: Richard L. Epstein; Lesław W. Szczerba

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.

Table of contents:

I. Classical Propositional Logic

II. Abstracting and Axiomatizing Classical Propositional Logic

III. The Language of Predicate Logic

IV. The Semantics of Classical Predicate Logic

V. Substitutions and Equivalences

VI. Equality

VII. Examples of Formalization

VIII. Functions

IX. The Abstraction of Models

X. Axiomatizing Classical Predicate Logic

XI. The Number of Objects in the Universe of a Model

XII. Formalizing Group Theory

XIII. Linear Orderings

XIV. Second-Order Classical Predicate Logic

XV. The Natural Numbers

XVI. The Integers and Rationals

XVII. The Real Numbers

XVIII. One-Dimensional Geometry

XIX. Two-Dimensional Euclidean Geometry

XX. Translations within Classical Predicate Logic

XXI. Classical Predicate Logic with Non-Referring Names

XXII. The Liar Paradox

XXIII. On Mathematical Logic and Mathematics

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classical Mathematical Logic The Semantic Foundations of Logic

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