Algebra Seminar talk
2014-12-05
Vera Fischer
Definable maximal cofinitary groups and large continuum
Abstract:
A cofinitary group is a subgroup of the group of all
permutations of the natural numbers, all non-identity elements of which
have only finitely many fixed points. A cofinitary group is maximal if it
is not properly contained in any other cofinitary group.
We will discuss the existence of nicely definable maximal cofinitary groups in the presence of large continuum and in particular, we will see the generic construction of a maximal cofinitary group with a $\Pi^1_2$ definable set of generators in the presence of $2^\omega=\aleph_2$.