Blog Archives

Topic Archive: modal logic of forcing

Set theory seminarFriday, April 11, 201410:00 amGC6417

George Leibman

Structural Connections Between a Forcing Class and its Modal Logic

Bronx Community College, CUNY

This talk is on recent work with Joel Hamkins and Benedikt Loewe on ways in which finite-frame properties of specific modal logics can be combined with assertions in ZFC to show that these modal logics are related to those which arise from interpreting Gamma-forcing extensions of a model of ZFC as possible worlds of a Kripke model, where Gamma can be any of several classes of notions of forcing.

George Leibman
Bronx Community College, CUNY
George Leibman is a professor in the Mathematics and Computer Science department at Bronx Community College, CUNY. He received his doctorate from the CUNY Graduate Center in 2004, under the direction of Joel Hamkins, and he conducts research in set theory, with a particular interest in the modal logic of forcing.
CUNY Logic WorkshopFriday, September 7, 201212:00 amGC 6417

Joel David Hamkins

Recent progress on the modal logic of forcing and grounds

The City University of New York

The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, with “true in all forcing extensions” and“true in some forcing extension” as the accompanying modal operators. In this modal language one may easily express sweeping general forcing principles, such as the assertion that every possibly necessary statement is necessarily possible, which is valid for forcing, or the assertion that every possibly necessary statement is true, which is the maximality principle, a forcing axiom independent of but equiconsistent with ZFC. Similarly, the dual modal logic of grounds concerns the modalities “true in all ground models” and “true in some ground model”. In this talk, I shall survey the recent progress on the modal logic of forcing and the modal logic of grounds. This is joint work with Benedikt Loewe and George Leibman.