Sequent logic of arithmetic decidability (Q1866903)
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scientific article; zbMATH DE number 1900011
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sequent logic of arithmetic decidability |
scientific article; zbMATH DE number 1900011 |
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Sequent logic of arithmetic decidability (English)
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23 April 2003
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This paper follows the works by \textit{H. Montgomery} and \textit{R. Routley} [Logique Anal. 11, 422-424 (1968; Zbl 0169.30003)] and \textit{I. L. Humberstone} [Notre Dame J. Formal Logic 36, 214-229 (1995; Zbl 0833.03004)]. The author proposes an axiomatics for the provability logic over GL, i.e. the logic which is complete in the interpretation of formulas of the form \(\vartriangleright A\) such as ``the assertion \(A\) is provable in Peano arithmetic''. Also sequent calculi are presented for the provability logics over K, K4 and GL.
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arithmetic solvability
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sequent logic
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Gödel-Löb logic
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provability logic
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