The spectrum of $\kappa$-maximal cofinitary groups

Vera Fischer (TU Wien):

For $\kappa$ an arbitrary regular uncountable cardinal we define the spectrum of $\kappa$-maximal cofinitary groups (abbreviated $\kappa$-mcg) as the set of all possible cardinalities of $\kappa$-mcg's.

Generalizing Blass's result on the spectrum of mad families on $\omega$, we provide sufficient conditions for a closed set of cardinals to be generically realized as the spectrum of $\kappa$-mcgs. We will conclude with some current directions of research and open questions.