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)
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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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Citations of this work

Passive induction and a solution to a Paris–Wilkie open question.Dan E. Willard - 2007 - Annals of Pure and Applied Logic 146 (2-3):124-149.
2007-2008 Winter Meeting of the Association for Symbolic Logic.Jeffrey Remmel - 2008 - Bulletin of Symbolic Logic 14 (3):402-411.
2006–07 Winter Meeting of the Association for Symbolic Logic.Marcia Groszek - 2007 - Bulletin of Symbolic Logic 13 (3):375-385.

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References found in this work

On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
On Herbrand consistency in weak arithmetic.Zofia Adamowicz & Paweł Zbierski - 2001 - Archive for Mathematical Logic 40 (6):399-413.

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