On provability logics with linearly ordered modalities
Logic
2012-10-18 v1
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).
Cite
@article{arxiv.1210.4809,
title = {On provability logics with linearly ordered modalities},
author = {Lev D. Beklemishev and David Fernández-Duque and Joost J. Joosten},
journal= {arXiv preprint arXiv:1210.4809},
year = {2012}
}