Notre Dame Journal of Formal Logic

A System of Complete and Consistent Truth

Volker Halbach

Abstract

To the axioms of Peano arithmetic formulated in a language with an additional unary predicate symbol T we add the rules of necessitation $\phi/T\,\overline{\phi }$ and conecessitation T $\,\overline{\phi }/\phi $ and axioms stating that T commutes with the logical connectives and quantifiers. By a result of McGee this theory is $\omega$-inconsistent, but it can be approximated by models obtained by a kind of rule-of-revision semantics. Furthermore we prove that FS is equivalent to a system already studied by Friedman and Sheard and give an analysis of its proof theory.

Article information

Source
Notre Dame J. Formal Logic Volume 35, Number 3 (1994), 311-327.

Dates
First available in Project Euclid: 21 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1040511340

Mathematical Reviews number (MathSciNet)
MR1326116

Digital Object Identifier
doi:10.1305/ndjfl/1040511340

Zentralblatt MATH identifier
0828.03030

Subjects
Primary: 03F25: Relative consistency and interpretations
Secondary: 03F30: First-order arithmetic and fragments 03F40: Gödel numberings and issues of incompleteness

Citation

Halbach, Volker. A System of Complete and Consistent Truth. Notre Dame J. Formal Logic 35 (1994), no. 3, 311--327. doi:10.1305/ndjfl/1040511340. http://projecteuclid.org/euclid.ndjfl/1040511340.


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References

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