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.
"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