# Symmetric extensions and models of ZF

**Date**: Monday 8 October 2018, 14:00 – 15:00**Location**: Roger Stevens LT 12 (10M.12)**Type**: Seminars, Pure Mathematics**Cost**: Free

#### Richard Matthews, University of Leeds. Part of the postgraduate logic seminar series.

In this introductory talk we will review the basic notions necessary to build a forcing extension M[G] of a model M of ZFC. From this we will see how, by restricting to a certain class of names, we can build a model of ZF which lies between M and M[G]. This model is called a symmetric extension of M and is useful in providing nice models for which the axiom of choice fails, sometimes very badly. If there is time we will also explore some of these models and the relationship between symmetric extensions and permutation models of ZFA, that is ZF with atoms.