The modal logic of forcing

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dc.creatorHamkins, Joel David
dc.creatorLoewe, Benedikt
dc.date2005-09-27
dc.date.accessioned2026-07-07T06:19:21Z
dc.date.available2026-07-07T06:19:21Z
dc.descriptionWhat 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.
dc.description31 pages
dc.identifierhttps://arxiv.org/abs/math/0509616
dc.identifierhttp://arxiv.org/abs/math/0509616
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95040
dc.subjectLogic
dc.subject03E40; 03B45
dc.titleThe modal logic of forcing
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