Classical Mathematical Logic: The Semantic Foundations of Logic

Classical Mathematical Logic: The Semantic Foundations of Logic

by Richard L. Epstein
     
 

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,

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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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Product Details

ISBN-13:
9780691123004
Publisher:
Princeton University Press
Publication date:
07/03/2006
Edition description:
New Edition
Pages:
544
Product dimensions:
7.24(w) x 10.06(h) x 1.34(d)

Table of Contents

IClassical propositional logic
IIAbstracting and axiomatizing classical propositional logic
IIIThe language of predicate logic
IVThe semantics of classical predicate logic
VSubstitutions and equivalences
VIEquality
VIIExamples of formalization
VIIIFunctions
IXThe abstraction on models
XAxiomatizing classical predicate logic
XIThe number of objects in the universe of a model
XIIFormalizing group theory
XIIILinear orderings
XIVSecond-order classical predicate logic
XVThe natural numbers
XVIThe integers and rationals
XVIIThe real numbers
XVIIIOne-dimensional geometry
XIXTwo-dimensional Euclidean geometry
XXTranslations with classical predicate logic
XXIClassical predicate logic with non-referring names
XXIIThe liar paradox
XXIIIOn mathematical logic and mathematics
AppThe completeness of classical predicate logic proved by Godel's method

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