Modal analysis of generalized Rosser sentences

Journal of Symbolic Logic 48 (4):986-999 (1983)

A modal theory Z using the Guaspari witness comparison signs $\leq, is developed. The theory Z is similar to, but weaker than, the theory R of Guaspari and Solovay. Nevertheless, Z proves the independence of the Rosser fixed-point. A Kripke semantics for Z is presented and some arithmetical interpretations of Z are investigated. Then Z is enriched to ZI by adding a new modality sign for interpretability and by axioms expressing some facts about interpretability of theories. Two arithmetical interpretations of ZI are presented. The proofs of the validity of the axioms of ZI in arithmetical interpretations use some strengthening of Solovay's result about interpretability in Godel-Bernays set theory
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DOI 10.2307/2273663
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References found in this work BETA

Rosser Sentences.D. Guaspari - 1979 - Annals of Pure and Applied Logic 16 (1):81.

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Faith & Falsity.Albert Visser - 2004 - Annals of Pure and Applied Logic 131 (1):103-131.
The Formalization of Interpretability.Albert Visser - 1991 - Studia Logica 50 (1):81 - 105.
A Course on Bimodal Provability Logic.Albert Visser - 1995 - Annals of Pure and Applied Logic 73 (1):109-142.

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