Classical Mathematical Logic: The Semantic Foundations of Logic

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Overview

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.

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Editorial Reviews

Zentralblatt MATH Database
[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

[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 - Siegfried J. Gottwald
[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.
From the Publisher

"[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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Product Details

  • ISBN-13: 9780691123004
  • Publisher: Princeton University Press
  • Publication date: 7/3/2006
  • Edition description: New Edition
  • Pages: 544
  • Product dimensions: 7.24 (w) x 10.06 (h) x 1.34 (d)

Meet the Author

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.

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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 on 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 with classical predicate logic
XXI Classical predicate logic with non-referring names
XXII The liar paradox
XXIII On mathematical logic and mathematics
App The completeness of classical predicate logic proved by Godel's method
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