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  • TWO NEW SERIES OF PRINCIPLES IN THE INTERPRETABILITY LOGIC OF ALL REASONABLE ARITHMETICAL THEORIES

  • EVAN GORIS, JOOST J. JOOSTEN
  • Journal:
    The Journal of Symbolic Logic / Volume 85 / Issue 1 / March 2020
    Published online by Cambridge University Press:
    12 December 2019, pp. 1-25
    Print publication:
    March 2020

  • 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 article 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.