Template iterations and maximal cofinitary groups

Vera Fischer, and Asger Törnquist. "Template iterations and maximal cofinitary groups." Fundamenta Mathematicae 230.3 (2015): 205-236. <http://eudml.org/doc/283159>.

@article{VeraFischer2015,
abstract = {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 $_g$, 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 $_p$, the minimal size of a maximal family of almost disjoint permutations, and $_e$, the minimal size of a maximal eventually different family, can be of countable cofinality.},
author = {Vera Fischer, Asger Törnquist},
journal = {Fundamenta Mathematicae},
keywords = {cardinal characteristics; maximal cofinitary groups; template forcing iterations},
language = {eng},
number = {3},
pages = {205-236},
title = {Template iterations and maximal cofinitary groups},
url = {http://eudml.org/doc/283159},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Vera Fischer
AU - Asger Törnquist
TI - Template iterations and maximal cofinitary groups
JO - Fundamenta Mathematicae
PY - 2015
VL - 230
IS - 3
SP - 205
EP - 236
AB - 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 $_g$, 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 $_p$, the minimal size of a maximal family of almost disjoint permutations, and $_e$, the minimal size of a maximal eventually different family, can be of countable cofinality.
LA - eng
KW - cardinal characteristics; maximal cofinitary groups; template forcing iterations
UR - http://eudml.org/doc/283159
ER -