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Book 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.

Book details

Book category Books in English Mathematics & science Mathematics Number theory

• Full title: Studies in Weak Arithmetics
• Author: Patrick Cegielski
• Language: English
• Binding: Paperback
• Number of pages: 221
• EAN: 9781575866024
• ISBN: 9781575866024
• ID: 06256998
• Publisher: Centre for the Study of Language & Information
• Weight: 304 g
• Dimensions: 229 × 152 × 13 mm
• Date of publishing: 10. August 2010

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