Fullness and mixing property for boolean valued models

29.04.2021 15:00 - 16:30

Moreno Pierobon (Università di Pisa, Italy)

Besides being one of the classical approaches to forcing, boolean valued models provide a flexible tool to produce a variety of structures.

In this talk, we will investigate in details the fullness property and the mixing property for boolean valued models. The former is necessary to control the semantics when quotienting a boolean valued model by an  ultrafilter. The latter implies the former and it is easier to check.

We will show that not every model is full, and the mixing property in not equivalent to fullness. Moreover, we will improve the classical Łoś Theorem for boolean valued models.

In the end, we will give a simple characterization of the mixing property using étalé spaces. This last result is an easy corollary of a more general study we made on the categorical equivalence between boolean valued models and presheaves.

This is a joint work with Matteo Viale.



online via Zoom