Overview

The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. In this volume, after a general presentation of weak arithmetics, the following topics are studied: the properties of integers of a real closed field equipped with exponentiation; conservation results for the induction schema restricted to first-order formulas with a finite number of alternations of quantifiers; a survey on a class of tools called pebble games; the fact that the reals e and pi have approximations expressed by first-order formulas using bounded quantifiers; properties of infinite pictures depending on the universe of sets used; a language that simulates in a sufficiently nice manner all  algorithms of a certain restricted class; the logical complexity of the axiom of infinity in some variants of set theory without the axiom of  foundation; and the complexity to determine whether a trace is included in another one.

Full Product Details

Author:   Patrick Cegielski
Publisher:   Centre for the Study of Language & Information
Imprint:   Centre for the Study of Language & Information
Volume:   No.196
Dimensions:   Width: 1.60cm , Height: 0.10cm , Length: 2.30cm
Weight:   0.312kg
ISBN:  

9781575866024

ISBN 10:   1575866021
Pages:   221
Publication Date:   15 December 2009
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

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Patrick Cegielski is professor at Universite Paris-Est Creteil-IUT de Senart Fontainebleau.

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