




Studies in Weak Arithmetics, Volume 1
CSLI, 2009 Paper: 9781575866024  eISBN: 9781575866826 Library of Congress Classification QA241.S824 2010 Dewey Decimal Classification 512.7
ABOUT THIS BOOK  AUTHOR BIOGRAPHY  TOC
ABOUT THIS BOOK
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 firstorder 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 firstorder 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. See other books on: Logic  Logic, Symbolic and mathematical  Mathematics  Studies  Volume 1 See other titles from CSLI 
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