Logic of Arithmetic

by Walter Felscher

Overview

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.

Product Details

ISBN-13:	9780367398576
Publisher:	Taylor & Francis
Publication date:	09/05/2019
Series:	Lectures on Mathematical Logic , #3
Pages:	312
Product dimensions:	6.00(w) x 9.00(h) x (d)

Table 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

Editorial Reviews

A complete representation of the current knowledge in Mathematical Logic in a detailed and precise manner.

Michael M. Richter