Studies in Weak Arithmetics: Volume 1: 196 (Lecture Notes) - Softcover

Cegielski, Patrick

 
9781575866024: Studies in Weak Arithmetics: Volume 1: 196 (Lecture Notes)
Softcover
ISBN 10: 1575866021 ISBN 13: 9781575866024
Publisher: Center for the Study of Language and Information, 2010

Synopsis

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.

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About the Author

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

"About this title" may belong to another edition of this title.

Publisher
Center for the Study of Language and Information
Publication date
2010
Language
English
ISBN 10 
1575866021
ISBN 13 
9781575866024
Binding
Paperback
Number of pages
221

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