MoL-2008-06:
Icard, Thomas
(2008)
*Models of the Polymodal Provability Logic.*
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## Abstract

This thesis on the polymodal provability logic GLP is divides into

three main sections. In the first section, we investigate relational

models of GLP. After presenting a simplified treatment of

Beklemishev's blow-up model construction, we exploit completeness for

such models to obtain a new, purely semantic proof that GLP_0, the

closed fragment of GLP, is complete with respect to Ignatiev's frame

U. Following this, we investigate formula definable subsets of U in

anticipation of our work in the next two sections.

In the second section, we explore the connection between U and the

canonical frame of GLP_0. Using the theory of descriptive frames, we

extend U to a frame that is isomorphic to the canonical frame, thus

obtaining a detailed definition of this object in terms of a

coordinate system developed in the first section.

Finally, in the last section, we explore topological models of

GLP. The central result of this section is an analog of the

Abashidze-Blass Theorem for GL, to the effect that GLP_0 enjoys

topological completeness with respect to a simply defined polytopology

on the ordinal epsilon_0 +1. This space can be seen as a condensed,

and much simplified, version of the canonical frame of GLP_0. We then

consider the possibility of an extension of this theorem to full

GLP. However, such an extension would require large cardinal

assumptions beyond ZFC, so we leave this further question for future

work.

All of this work can be seen as an effort to overcome (and better

explain) the fact that GLP is frame incomplete.

Item Type: | Report |
---|---|

Report Nr: | MoL-2008-06 |

Series Name: | Master of Logic Thesis (MoL) Series |

Year: | 2008 |

Date Deposited: | 12 Oct 2016 14:38 |

Last Modified: | 12 Oct 2016 14:38 |

URI: | https://eprints.illc.uva.nl/id/eprint/801 |

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