Moving up and down in the generic multiverse
Logic
2012-08-28 v1
Abstract
We give a brief account of 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 called the modal logic of forcing and was studied by us in earlier work. The fragment of the second relation is called 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.
Keywords
Cite
@article{arxiv.1208.5061,
title = {Moving up and down in the generic multiverse},
author = {Joel David Hamkins and Benedikt Löwe},
journal= {arXiv preprint arXiv:1208.5061},
year = {2012}
}
Comments
10 pages. Extended abstract. Questions and commentary concerning this article can be made at http://jdh.hamkins.org/up-and-down-in-the-generic-multiverse/