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The consistency of 𝔟 = κ and 𝔰 = κ⁺

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Fischer V., Steprāns J.

Fundamenta Mathematicae

2008

tom 201

nr 3

283-293

Using finite support iteration of ccc partial orders we provide a model of 𝔟 = κ < 𝔰 = κ⁺ for κ an arbitrary regular, uncountable cardinal.

Template iterations and maximal cofinitary groups

100%

Fischer V., Törnquist A.

Fundamenta Mathematicae

2015

tom 230

nr 3

205-236

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.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Fischer V.

1 Steprāns J.

1 Törnquist A.

1 2015

1 2008

Wyniki wyszukiwania

The consistency of 𝔟 = κ and 𝔰 = κ⁺

Template iterations and maximal cofinitary groups