Modal logics of forcing classes

17^th April 2012, 15:00 Ashton Lecture Theatre
Prof. Benedikt Loewe
Institute for Logic, Language and Computation
University of Amsterdam
NL

Abstract

In 2008, Hamkins and Loewe determined the "modal logic of forcing", the set
of modal statements that are valid under the interpretation of "possibly p" as
"there is a forcing extension of the set-theoretic universe such that p is true".
The modal logic of forcing is S4.2. We discuss structural relations between
closure properties of classes of 'forcings' (i.e., Boolean algebras used to
extend the set-theoretic universe) and the corresponding modal logics.