Template iterations and maximal cofinitary groups

Abstract

The main result of the present paper is that ${\mathfrak{a}}_g$, the minimal size of maximal cofinitary group, can be of countable cofinality. To prove this we define a natural poset for adding a maximal cofinitary group of a given cardinality, which enjoys certain combinatorial properties allowing it to be used within a similar template forcing construction. Additionally we obtain that ${\mathfrak{a}}_p$, the minimal size of a maximal family of almost disjoint permutations, and ${\mathfrak{a}}_e$, the minimal size of a maximal eventually different family, can be of countable cofinality.

arXiv comment24 pages