Miha Habič: Surgery and generic coding

Dear all,

The seminar meets on Wednesday October 10th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Note that there will be no seminar on Wednesday October 17th.

Program: Miha Habič — 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.


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