Moving up and down in the generic multiverse

Abstract

We investigate the modal logic of the generic multiverse which is a bimodal logic with operators corresponding to the relations "is a forcing extension of" and "is a ground model of". The fragment of the first relation is the modal logic of forcing and was studied by the authors in earlier work. The fragment of the second relation is the modal logic of grounds and will be studied here for the first time. In addition, we discuss which combinations of modal logics are possible for the two fragments. © 2013 Springer-Verlag Berlin Heidelberg.