Classical Mathematical Logic

The Semantic Foundations of Logic

By: Richard L. Epstein, Leslaw W. Szczerba (Contribution by)

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Hardcover | 27 June 2006

At a Glance

Hardcover
544 Pages

Age
22+

Dimensions(cm)
25.4 x 17.7 x 254

Hardcover

RRP $250.00

$178.99

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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.

Industry Reviews

"[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

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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 on 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 with classical predicate logic
Classical predicate logic with non-referring names
The liar paradox
On mathematical logic and mathematics
The completeness of classical predicate logic proved by Godel's method
Table of Contents provided by Blackwell. All Rights Reserved.

Classical Mathematical Logic

The Semantic Foundations of Logic

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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