Template iterations and maximal cofinitary groups

• Autorzy: Vera Fischer , Asger Törnquist
• Języki publikacji: 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.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 230
• Numer: 3
• Strony: 205-236

Daty

wydano

2015

Twórcy

autor

Vera Fischer

• Institute of Discrete Mathematics, and Geometry, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria

autor

Asger Törnquist

• Department of Mathematical Sciences, University of Copenhagen, Universitetspark 5, 2100 København, Denmark

Identyfikatory

DOI

10.4064/fm230-3-1