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

Willard, Dan E.

Willard, Dan E.

J. Symbolic Logic, Tome 71 (2006) no. 1, p. 1189-1199 / Harvested from Project Euclid

Résumé

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.

Publié le : 2006-12-14
Classification:

@article{1164060451,
     author = {Willard, Dan E.},
     title = {On the available partial respects in which an axiomatization for real valued arithmetic can recognize its consistency},
     journal = {J. Symbolic Logic},
     volume = {71},
     number = {1},
     year = {2006},
     pages = { 1189-1199},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1164060451}
}

Willard, Dan E. On the available partial respects in which an axiomatization for real valued arithmetic can recognize its consistency. J. Symbolic Logic, Tome 71 (2006) no. 1, pp.  1189-1199. http://gdmltest.u-ga.fr/item/1164060451/