Ernest Schimmerling

Mathematical logic seminar - February 16, 2006

Time: 12 - 1:20 p.m.

Room: DH 1209

Speaker:     Kohei Kishida   
Doctoral candidate
Department of Philosophy
University of Pittsburgh

Title: Topological Semantics for Modal Logic

Abstract: As Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the ``necessity'' operation is modeled by taking the interior of an arbitrary subset of a topological space. This talk will show how to extend this interpretation from propositional to first-order logic by using the topos of all sheaves on a space, or its equivalent notion of local homeomorphisms.