Well-orders in the transfinite Japaridze algebra II: Turing progressions and their well-orders

David Fernández-Duque; Joost J. Joosten

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arXiv · 1204.4743

Well-orders in the transfinite Japaridze algebra II: Turing progressions and their well-orders

David Fernández-Duque·Joost J. Joosten

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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.

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BibTeX RIS

David Fernández-Duque, Joost J. Joosten. 2013-12-20. Well-orders in the transfinite Japaridze algebra II: Turing progressions and their well-orders. https://arxiv.org/abs/1204.4743

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