Notre Dame Journal of Formal Logic

A System of Complete and Consistent Truth

Volker Halbach


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

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

First available in Project Euclid: 21 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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