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arXiv · 1210.4809

On provability logics with linearly ordered modalities

Lev D. Beklemishev·David Fernández-Duque·Joost J. Joosten
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Abstract

We introduce the logics GLP(\Lambda), a generalization of Japaridze's polymodal provability logic GLP(\omega) where \Lambda is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP(\omega) yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP(\Lambda) and the decidability of GLP(\Lambda) for recursive orderings \Lambda. Further, we give a restricted axiomatization of the variable-free fragment of GLP(\Lambda).

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Lev D. Beklemishev, David Fernández-Duque, Joost J. Joosten. 2012-10-17. On provability logics with linearly ordered modalities. https://arxiv.org/abs/1210.4809

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