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.
By:
Walter Felscher
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions:
Height: 229mm,
Width: 152mm,
Weight: 453g
ISBN: 9780367398576
ISBN 10: 0367398575
Pages: 312
Publication Date: 05 September 2019
Audience:
College/higher education
,
Professional and scholarly
,
A / AS level
,
Further / Higher Education
Format: Paperback
Publisher's Status: Active
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
