A Concise Introduction to Mathematical Logic

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Springer Science & Business Media, Sep 28, 2006 - Mathematics - 256 pages
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While there are already several well known textbooks on mathematical logic this book is unique in treating the material in a concise and streamlined fashion. This allows many important topics to be covered in a one semester course. Although the book is intended for use as a graduate text the first three chapters can be understood by undergraduates interested in mathematical logic. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text.

 

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Contents

The Foundations of Logic Programming 4 1 Term Models and Horn Formulas 4 2 Propositional Resolution 4 3 Unification 4 4 Logic Programming ...
4
Elements of Model Theory 5 1 Elementary Extensions 5 2 Complete and κCategorical Theories 5 3 Ehrenfeuchts game 5 4 Embedding and Characte...
5
Incompleteness and Undecidability 6 1 Recursive and Primitive Recursive Functions 6 2 Arithmetization 6 3 Representability of Arithmetical Predicat...
6
On the Theory of SelfReference 7 1 The Derivability Conditions 7 2 The Theorems of Gödel and Löb 7 3 The Provability Logic G 7 4 The Modal T...
7
Hints to the Exercises
24
1
33
3
41
5
62
2
71
7
85
Hilbert Calculi
95
Literature
98
67
252
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