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On the available partial respects in which an axiomatization for real valued arithmetic can recognize its consistency

Published online by Cambridge University Press:  12 March 2014

Dan E. Willard
Dan E. Willard*
Affiliation:
Departments of Computer Science and Mathematics, University of Albany, Albany, NY 12222, USA, E-mail: dew@cs.albany.edu, URL: http://www.cs.albany.edu/~dew
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Abstract

Gödel's Second Incompleteness Theorem states axiom systems of sufficient strength are unable to verify their own consistency. We will show that axiomatizations for a computer's floating point arithmetic can recognize their cut-free consistency in a stronger respect than is feasible under integer arithmetics. This paper will include both new generalizations of the Second Incompleteness Theorem and techniques for evading it.

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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 4 , December 2006 , pp. 1189 - 1199
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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