## 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

https://projecteuclid.org/euclid.ndjfl/1040511340

Digital Object Identifier
doi:10.1305/ndjfl/1040511340

Mathematical Reviews number (MathSciNet)
MR1326116

Zentralblatt MATH identifier
0828.03030

#### 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. https://projecteuclid.org/euclid.ndjfl/1040511340

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