The modal logic of σ-centered forcing

Speaker: Ur Benari-Tish

Abstract: Modal logic is used to study various modalities, i.e. various ways in which statements can be true, the most notable of which are the modalities of necessity and possibility. In set theory, there are different ways of saying when a statement is necessary or possible. One such way is saying that a statement is necessary if it is true in any forcing extension, and possible if it is true in some forcing extension. This gives rise to the so-called "Modal logic of forcing" - the modal statements which can always be proven in ZFC under this interpretation. We can also restrict ourselves to some class of forcing notions satisfying a given property, and ask what is its modal logic.

In this talk we will present the main tools used in the study of the these modal logics, and, as time permits, sketch the proof that the modal logic of σ-centered forcing is the modal theory known as S4.2.

Speaker: Ur Benari-Tish

Abstract: Modal logic is used to study various modalities, i.e. various ways in which statements can be true, the most notable of which are the modalities of necessity and possibility. In set theory, there are different ways of saying when a statement is necessary or possible. One such way is saying that a statement is necessary if it is true in any forcing extension, and possible if it is true in some forcing extension. This gives rise to the so-called "Modal logic of forcing" - the modal statements which can always be proven in ZFC under this interpretation. We can also restrict ourselves to some class of forcing notions satisfying a given property, and ask what is its modal logic.

In this talk we will present the main tools used in the study of the these modal logics, and, as time permits, sketch the proof that the modal logic of σ-centered forcing is the modal theory known as S4.2.

## Date:

Wed, 21/12/2016 - 16:00 to 18:00

## Location:

Ross 70