Open Access
2001 The Fixed Point Property in Modal Logic
Lorenzo Sacchetti
Notre Dame J. Formal Logic 42(2): 65-86 (2001). DOI: 10.1305/ndjfl/1054837934


This paper deals with the modal logics associated with (possibly nonstandard) provability predicates of Peano Arithmetic. One of our goals is to present some modal systems having the fixed point property and not extending the Gödel-Löb system GL. We prove that, for every $ n\geq 2, K+\square(\square^{n-1}p\rightarrow p)\rightarrow\square p$ has the explicit fixed point property. Our main result states that every complete modal logic L having the Craig's interpolation property and such that $ L\vdash\Delta(\nabla(p)\rightarrow p)\rightarrow\Delta(p)$, where $ \nabla(p)$ and $ \Delta(p)$ are suitable modal formulas, has the explicit fixed point property.


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Lorenzo Sacchetti. "The Fixed Point Property in Modal Logic." Notre Dame J. Formal Logic 42 (2) 65 - 86, 2001.


Published: 2001
First available in Project Euclid: 5 June 2003

zbMATH: 1031.03039
MathSciNet: MR1993391
Digital Object Identifier: 10.1305/ndjfl/1054837934

Primary: 03B45 , 03F40
Secondary: 03F30 , 03F45

Keywords: Fixed points , modal logic , provability predicates

Rights: Copyright © 2001 University of Notre Dame

Vol.42 • No. 2 • 2001
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