A Friendly Introduction to Mathematical Logic

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Lulu.com, 2015 - Computer logic - 365 pages
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At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.
 

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Contents

Structures and Languages
1
Deductions
41
Completeness and Compactness
73
Incompleteness from Two Points of View
103
Syntactic IncompletenessGroundwork
117
The Incompleteness Theorems
169
Computability Theory
195
Summing Up Looking Ahead
265
Just Enough Set Theory to Be Dangerous
279
Solutions to Selected Exercises
283
Bibliography
359
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