Jörg Brendle (2003) used Hechler’s forcing notion for adding a maximal almost disjoint family along an appropriate template forcing construction to show that (the minimal size of a maximal almost disjoint family) can be of countable cofinality. The main result of the present paper is that , the minimal size of a 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 find that , the minimal size of a maximal family of almost disjoint permutations, and , the minimal size of a maximal eventually different family, can be of countable cofinality.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-3-1,
author = {Vera Fischer and Asger T\"ornquist},
title = {Template iterations and maximal cofinitary groups},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {205-236},
zbl = {06438020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-3-1}
}
Vera Fischer; Asger Törnquist. Template iterations and maximal cofinitary groups. Fundamenta Mathematicae, Tome 228 (2015) pp. 205-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-3-1/