# 2020 seminar talk: Fake Reflection

Talk held by Miguel Moreno (Bar-Ilan University, Ramat Gan, Tel Aviv, Israel) at the KGRC seminar on 2020-01-23.

### Abstract

Motivated from many results in generalized descriptive set theory, Filter Reflection (aka Fake Reflection) is an abstract version of reflection compatible with large cardinals, forcing axioms, but also V=L.

In this talk we will present the motivation and definition of filter reflection, we will explain how to force filter reflection and how to force its failure. We will also show some applications and properties of filter reflection, e.g. the consistency of “$E_{\omega_1}^\kappa$ filter reflects to a subset of $E_{\omega}^\kappa$”.

This is a joint work with Gabriel Fernandes and Assaf Rinot.