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Fundamenta Mathematicae

2015 | 230 | 3 | 205-236

Template iterations and maximal cofinitary groups

EN

Abstrakty

EN
Jörg Brendle (2003) used Hechler's forcing notion for adding a maximal almost disjoint 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 $𝔞_g$, 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 $𝔞_p$, the minimal size of a maximal family of almost disjoint permutations, and $𝔞_e$, the minimal size of a maximal eventually different family, can be of countable cofinality.

205-236

wydano
2015

Twórcy

autor
• Institute of Discrete Mathematics, and Geometry, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria
autor
• Department of Mathematical Sciences, University of Copenhagen, Universitetspark 5, 2100 København, Denmark