Fundamentals of Mathematical Logic

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CRC Press, Oct 8, 2018 - Mathematics - 894 pages
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This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.
 

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Contents

Introduction
1
Propositional Logic and Other Fundamentals
13
FirstOrder Logic
83
Completeness and Compactness
193
Incompleteness and Undecidability
309
Topics in Definability
393
Set Theory
455
Model Theory
655
Recursion Theory
733
References
821
Item References
829
Symbol Index
835
Subject Index
855
Copyright

Other editions - View all

Fundamentals of Mathematical Logic
Peter G. Hinman
Limited preview - 2018
Fundamentals of Mathematical Logic
Peter G. Hinman
Snippet view - 2005

Common terms and phrases

algebra assignment assume atomic axiomatizable axioms Boolean called cardinal Chapter Clearly closed Compactness complete computation condition consider consistent constant symbols construction Corollary countable course decidable defined Definition denote easily effectively elements enumerable equivalent establish exactly example Exercise exists expressions extension fact Finally finite follows formal formula function function F give given hence holds hypothesis immediate induction infinite interpretable isomorphic L-sentences language least Lemma logic marked mathematical natural Note notion numbers ordering otherwise partial particular preceding Proof Proposition prove recursive recursive function relation result satisfied sentence sequence set operation simple stage structure subset Suppose symbols Theorem theory transitive true truth unique universe variables verify write

About the author (2018)

Peter G. Hinman earned his B.A. in mathematics from Harvard University in 1959. He studied mathematics at the graduate level in Berkeley at the University of California. In 1966, under the guidance of Professor John Addison, he received his Ph.D. in Mathematical Logic with a particular focus on Recursion Theory. He is currently a professor at the University of Michigan where he has taught since 1966 and advised seven successful Ph.D. students. In 1978 he published his first book Recursion-Theoretic Hierarchies.

Bibliographic information

QR code for Fundamentals of Mathematical Logic
TitleFundamentals of Mathematical Logic
AuthorPeter G. Hinman
PublisherCRC Press, 2018
ISBN1439864276, 9781439864272
Length894 pages
Subjects › 

Mathematics / General
Mathematics / Set Theory
  
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