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.
Citation
Volker Halbach. "A System of Complete and Consistent Truth." Notre Dame J. Formal Logic 35 (3) 311 - 327, /Summer 1994. https://doi.org/10.1305/ndjfl/1040511340
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