Studies in weak arithmetics
著者
書誌事項
Studies in weak arithmetics
（CSLI lecture notes, no. 196,
CSLI Publications, c2010-
- [v. 1]
- v. 3
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注記
Vol. 3: Edited by Patrick Cégielski, Ali Enayat, Roman Kossak
Includes bibliographical references
内容説明・目次
- 巻冊次
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[v. 1] ISBN 9781575866024
内容説明
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.
- 巻冊次
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v. 3 ISBN 9781575869537
内容説明
The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. This third volume in the weak arithmetics collection contains nine substantive papers based on lectures delivered during the two last meetings of the conference series Journees sur les Arithmetiques, held in 2014 at the University of Gothenburg, Sweden, and in 2015 at the City University of New York Graduate Center.
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