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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/161941
Two new series of principles in the interpretability logic of all reasonable arithmetical theories
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The provability logic of a theory T captures the structural behavior of formalized provability in T as provable in T itself. Like provability, one can formalize the notion of relative interpretability giving rise to interpretability logics. Where provability logics are the same for all moderately sound theories of some minimal strength, interpretability logics do show variations. The logic IL(All) is defined as the collection of modal principles that are provable in any moderately sound theory of some minimal strength. In this paper we raise the previously known lower bound of IL(All) by exhibiting two series of principles which are shown to be provable in any such theory. Moreover, we compute the collection of frame conditions for both series.
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GORIS, Evan and JOOSTEN, Joost J. Two new series of principles in the interpretability logic of all reasonable arithmetical theories. Journal of Symbolic Logic. 2020. Vol. 85, num. 1, pags. 1-25. ISSN 0022-4812. [consulted: 13 of October of 2026]. Available at: https://hdl.handle.net/2445/161941