The logic of π1-conservativity

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Archive for Mathematical Logic 30 (2):113-123 (1990)
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Abstract

We show that the modal prepositional logicILM (interpretability logic with Montagna's principle), which has been shown sound and complete as the interpretability logic of Peano arithmetic PA (by Berarducci and Savrukov), is sound and complete as the logic ofπ 1-conservativity over eachbE 1-sound axiomatized theory containingI⌆ 1 (PA with induction restricted tobE 1-formulas). Furthermore, we extend this result to a systemILMR obtained fromILM by adding witness comparisons in the style of Guaspari's and Solovay's logicR (this will be done in a separate continuation of the present paper)

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10.1007/bf01634981

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Citations of this work

The formalization of interpretability.Albert Visser - 1991 - Studia Logica 50 (1):81 - 105.
Transductions in arithmetic.Albert Visser - 2016 - Annals of Pure and Applied Logic 167 (3):211-234.

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References found in this work

Self-Reference and Modal Logic.George Boolos & C. Smorynski - 1988 - Journal of Symbolic Logic 53 (1):306.
Fragments of arithmetic.Wilfried Sieg - 1985 - Annals of Pure and Applied Logic 28 (1):33-71.
Modal analysis of generalized Rosser sentences.Vítězslav Švejdar - 1983 - Journal of Symbolic Logic 48 (4):986-999.
Self-Reference and Modal Logic.[author unknown] - 1987 - Studia Logica 46 (4):395-398.
Rosser sentences.D. Guaspari - 1979 - Annals of Mathematical Logic 16 (1):81.

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