Fri Sep 11, 2015
60 Evans Hall, 4:10–6 PM
Thomas Icard (Assistant Professor of Philosophy and Symbolic Systems, Stanford University)
A Survey on Topological Semantics for Provability Logics
This will be a survey of ideas and results on topological interpretations of provability logics, especially polymodal provability logics. Esakia first proved completeness for the basic Gödel-Löb logic of provability with respect to scattered spaces. Abashidze and Blass (independently) proved completeness w.r.t. a particular scattered space defined on the ordinal omega^omega. I will discuss older work of my own that extended the Abashidze-Blass result to a polymodal provability logic, which is complete with respect to a polytopological space on epsilon_0. I will then discuss more recent developments, including work by Beklemishev, Fernandez, Joosten, Gabelaia, Aguilera, and others, generalizing and improving upon much of this.