Well-orders in the transfinite Japaridze algebra II: Turing progressions and their well-orders
Logic
2013-12-23 v2
Abstract
We study transfinite extensions of Japaridze's provability logic GLP and the well-founded relations that naturally occur within them. Every ordinal induces a partial order over the class of "words," which are iterated consistency statements expressible within GLP. Well-ordered restrictions of these partial orders have been studied previously; in this paper we consider the unrestricted partial orders, which are no longer linear but remain well-founded. These unrestricted partial orders bear important repercussions on modal semantics for GLP and on Turing progressions.
Keywords
Cite
@article{arxiv.1204.4743,
title = {Well-orders in the transfinite Japaridze algebra II: Turing progressions and their well-orders},
author = {David Fernández-Duque and Joost J. Joosten},
journal= {arXiv preprint arXiv:1204.4743},
year = {2013}
}
Comments
Extension of previous version by Section 10, some new proofs and theorems