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ON THE AVAILABLE PARTIAL RESPECTS IN WHICH AN AXIOMATIZATION FOR REAL VALUED ARITHMETIC CAN RECOGNIZE ITS CONSISTENCY.

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 ari...

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Published in:Journal of Symbolic Logic Vol. 71; no. 4; pp. 1189 - 1200
Main Author: Willard, Dan E.
Format: Article
Published: Cambridge University Press Dec2006
Subjects:
Incompleteness theorems
Gödel's theorem
Axioms
Foundations of geometry
Foundations of arithmetic
Mathematical logic
Online Access:View this record in EBSCOhost
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      dt: Dec2006
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        atl: ON THE AVAILABLE PARTIAL RESPECTS IN WHICH AN AXIOMATIZATION FOR REAL VALUED ARITHMETIC CAN RECOGNIZE ITS CONSISTENCY.
      aug:
        au: Willard, Dan E.
        affil: Department of Computer Science and Mathematics, University of Albany, Albany, NY 12222, USA
      su:
        Incompleteness theorems
        Gödel's theorem
        Axioms
        Foundations of geometry
        Foundations of arithmetic
        Mathematical logic
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        subj:
          Incompleteness theorems
          Gödel's theorem
          Axioms
          Foundations of geometry
          Foundations of arithmetic
          Mathematical logic
      ab: 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.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
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          year: 2006
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