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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: [email protected], 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.

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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