On the available partial respects in which an axiomatization for real valued arithmetic can recognize its consistency
Dan E. Willard · Journal of Symbolic Logic · 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.