October 12
Miha Habič, Czech Technical University in Prague/Charles University
Surgery and generic coding

There has been some interest recently in nonamalgamability phenomena between countable models of set theory, and forcing extensions of a fixed model in particular. Nonamalgamability is typically achieved by coding some forbidden object between a collection of models in such a way that each model on its own remains oblivious, but some combination of them can recover the forbidden information.

In this talk we will examine the problem of coding arbitrary information into a generic filter, focusing on two particular examples. First, I will present some results of joint work with Jonathan Verner where we consider surgical modifications to Cohen reals and sets of indices where such modifications are always possible. Later, I will discuss a recent result of S. Friedman and Hathaway where they achieve, using different coding, nonamalgamability between arbitrary countable models of set theory of the same height.