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

Journal of Symbolic Logic 71 (4):1189-1199 (2006)
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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