Mathematical Logic: An Introduction to Model Theory (Mathematical Concepts and Methods in Science and Engineering)

Lightstone, A.

ISBN 10: 1461587522 / ISBN 13: 9781461587521

Published by Springer, 2012

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Bibliographic Details

• Title: Mathematical Logic: An Introduction to Model Theory (Mathematical Concepts and Methods in Science and Engineering)
• Publisher: Springer
• Publication Date: 2012
• Language: English
• ISBN 10: 1461587522
• ISBN 13: 9781461587521
• Binding: Soft cover
• Condition: New

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Synopsis

Before his death in March, 1976, A. H. Lightstone delivered the manu­ script for this book to Plenum Press. Because he died before the editorial work on the manuscript was completed, I agreed (in the fall of 1976) to serve as a surrogate author and to see the project through to completion. I have changed the manuscript as little as possible, altering certain passages to correct oversights. But the alterations are minor; this is Lightstone's book. H. B. Enderton vii Preface This is a treatment of the predicate calculus in a form that serves as a foundation for nonstandard analysis. Classically, the predicates and variables of the predicate calculus are kept distinct, inasmuch as no variable is also a predicate; moreover, each predicate is assigned an order, a unique natural number that indicates the length of each tuple to which the predicate can be prefixed. These restrictions are dropped here, in order to develop a flexible, expressive language capable of exploiting the potential of nonstandard analysis. To assist the reader in grasping the basic ideas of logic, we begin in Part I by presenting the propositional calculus and statement systems. This provides a relatively simple setting in which to grapple with the some­ times foreign ideas of mathematical logic. These ideas are repeated in Part II, where the predicate calculus and semantical systems are studied.