Studies in Weak Arithmetics, Volume 1: Volume 1 Contributor(s): Cégielski, Patrick (Editor) |
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ISBN: 1575866021 ISBN-13: 9781575866024 Publisher: Center for the Study of Language and Informat OUR PRICE: $39.60 Product Type: Paperback - Other Formats Published: December 2009 |
Additional Information |
BISAC Categories: - Computers | Computer Science - Mathematics | Number Theory - Philosophy | Logic |
Dewey: 512.7 |
LCCN: 2009048021 |
Series: Lecture Notes |
Physical Information: 221 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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. |
Contributor Bio(s): Cegielski, Patrick: - Patrick Cégielskiis professor in the Département Informatique at Université Paris-Est Créteil. |