Template iterations and maximal cofinitary groups

Vera Fischer, Asger Törnquist
<span title="">2015</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yeobluctzze7rfwekxs7sx2ayy" style="color: black;">Fundamenta Mathematicae</a> </i> &nbsp;
In [2] , Jörg Brendle used Hechler's forcing notion for adding a maximal almost family along an appropriate template forcing construction to show that a (the minimal size of a maximal almost disjoint family) can be of countable cofinality. The main result of the present paper is that ag, 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
more &raquo; ... ial properties allowing it to be used within a similar template forcing construction. Additionally we obtain that ap, the minimal size of a maximal family of almost disjoint permutations, and ae, the minimal size of a maximal eventually different family, can be of countable cofinality.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/fm230-3-1">doi:10.4064/fm230-3-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/znnpgvg3fjd4zawms6cu2d5zxe">fatcat:znnpgvg3fjd4zawms6cu2d5zxe</a> </span>
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