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December 2006 On the available partial respects in which an axiomatization for real valued arithmetic can recognize its consistency
Dan E. Willard
J. Symbolic Logic 71(4): 1189-1199 (December 2006). DOI: 10.2178/jsl/1164060451

Abstract

Gödel’s Second Incompleteness Theorem states axiom systems ofsufficient strength are unable to verify their own consistency. Wewill show that axiomatizations for a computer’s floating pointarithmetic can recognize their cut-free consistency in a strongerrespect than is feasible under integer arithmetics. This paperwill include both new generalizations of the Second IncompletenessTheorem and techniques for evading it.

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Dan E. Willard. "On the available partial respects in which an axiomatization for real valued arithmetic can recognize its consistency." J. Symbolic Logic 71 (4) 1189 - 1199, December 2006. https://doi.org/10.2178/jsl/1164060451

Information

Published: December 2006
First available in Project Euclid: 20 November 2006

zbMATH: 1109.03068
MathSciNet: MR2275855
Digital Object Identifier: 10.2178/jsl/1164060451

Rights: Copyright © 2006 Association for Symbolic Logic

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Vol.71 • No. 4 • December 2006
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