## Journal of Symbolic Logic

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

Dan E. Willard

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 71, Issue 4 (2006), 1189-1199.

Dates
First available in Project Euclid: 20 November 2006

https://projecteuclid.org/euclid.jsl/1164060451

Digital Object Identifier
doi:10.2178/jsl/1164060451

Mathematical Reviews number (MathSciNet)
MR2275855

Zentralblatt MATH identifier
1109.03068

#### Citation

Willard, Dan E. On the available partial respects in which an axiomatization for real valued arithmetic can recognize its consistency. J. Symbolic Logic 71 (2006), no. 4, 1189--1199. doi:10.2178/jsl/1164060451. https://projecteuclid.org/euclid.jsl/1164060451

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