Logic of Arithmetic

Front Cover
CRC Press, May 30, 2000 - Mathematics - 312 pages
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For propositional logic it can be decided whether a formula has a deduction from a finite set of other formulas. This volume begins with a method to decide this for the quantified formulas of those fragments of arithmetic which express the properties of order-plus-successor and of order-plus-addition (Pressburger arithmetic). It makes use of an algorithm eliminating quantifiers which, in turn, is also applied to obtain consistency proofs for these fragments.
 

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Contents

Consistency Decidability Completeness for the Arithmetic
10
Consistency Decidability Completeness for the Arithmetic
34
Introduction to Chapters 39
56
Undefinability and Incompleteness General Theory
71
Elementary and Primitive Recursive Functions
99
Recursive Relations andRecursive Functions
132
The Arithmetization of Syntax
155
Consequences of Arithmetization
165
Dependences
187
Axioms for Arithmetic
190
Peano Arithmetic PA and its Expansion PR
219
Unprovability of Consistency
255
Epilogue
292
9
298
Index of symbolic notations
299
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