Logic of Arithmetic

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.

List of contents

1. Consistency, Decidability, Completeness for the Arithmetic of Order with Successor 2. Consistency, Decidability, Completeness for the Arithmetic of Addition and Order 3. Antinomies, Pseudomenos, and Their Analysis 4. Undefinability and Incompleteness, General Theory 5.Elementary and Primitive Recursive Functions 6. Recursive Relations and Recursive Functions 7. The Arithmitization of Syntax 8. Consequences of Arithmetization 9. Axioms for Arithmetic 10. Peano Arithmetic PA and Its Expansion PR 11. Unprovability of Consistency

About the author

Felscher, Walter

Product details

• Authors: Walter Felscher, Felscher Walter
• Publisher: Taylor and Francis
• Languages: English
• Product format: Hardback
• Released: 30.05.2000
• EAN: 9789056992682
• ISBN: 978-90-5699-268-2
• No. of pages: 312
• Weight: 740 g
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; MATHEMATICS / Logic, MATHEMATICS / Set Theory, Mathematical logic, Set theory