The modal logic of forcing

@misc{citeulike:2521250, abstract = {What are the most general principles in set theory relating forceability and truth? As with Solovay's celebrated analysis of provability, both this question and its answer are naturally formulated with modal logic. We aim to do for forceability what Solovay did for provability. A set theoretical assertion psi is forceable or possible, if psi holds in some forcing extension, and necessary, if psi holds in all forcing extensions. In this forcing interpretation of modal logic, we establish that if ZFC is consistent, then the ZFC-provable principles of forcing are exactly those in the modal theory known as S4.2.}, author = {Hamkins, Joel D. and Loewe, Benedikt }, citeulike-article-id = {2521250}, eprint = {math/0509616}, keywords = {modal-logic}, month = {Sep}, posted-at = {2008-03-12 15:17:45}, priority = {2}, title = {The modal logic of forcing}, url = {http://arxiv.org/abs/math/0509616}, year = {2005} }

TY - ELEC ID - citeulike:2521250 L3 - citeulike-article-id:2521250 TI - The modal logic of forcing N2 - What are the most general principles in set theory relating forceability and truth? As with Solovay's celebrated analysis of provability, both this question and its answer are naturally formulated with modal logic. We aim to do for forceability what Solovay did for provability. A set theoretical assertion psi is forceable or possible, if psi holds in some forcing extension, and necessary, if psi holds in all forcing extensions. In this forcing interpretation of modal logic, we establish that if ZFC is consistent, then the ZFC-provable principles of forcing are exactly those in the modal theory known as S4.2. KW - modal-logic AU - Hamkins, Joel AU - Loewe, Benedikt PY - 2005/Sep/27/ UR - http://arxiv.org/abs/math/0509616 ER -