Displaying similar documents to “Covering ω ω by special Cantor sets”

On ω 2 -saturated families

Lajos Soukup (1991)

Commentationes Mathematicae Universitatis Carolinae

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If there is no inner model with measurable cardinals, then for each cardinal λ there is an almost disjoint family 𝒜 λ of countable subsets of λ such that every subset of λ with order type ≥ ω 2 contains an element of 𝒜 λ .

Pcf theory and cardinal invariants of the reals

Lajos Soukup (2011)

Commentationes Mathematicae Universitatis Carolinae

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The additivity spectrum ADD ( ℐ ) of an ideal ℐ ⊂ 𝒫 ( I ) is the set of all regular cardinals κ such that there is an increasing chain { A α : α < κ } ⊂ ℐ with ⋃ α < κ A α ∉ ℐ . We investigate which set A of regular cardinals can be the additivity spectrum of certain ideals. Assume that ℐ = ℬ or ℐ = 𝒩 , where ℬ denotes the σ -ideal generated by the compact subsets of the Baire space ω ω , and 𝒩 is the ideal of the null sets. We show that if A is a non-empty progressive set of uncountable regular cardinals and pcf ( A ) = A , then ADD ( ℐ ) = A in some c.c.c generic extension...

On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique

Alejandro Ramírez-Páramo (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we make use of the Pol-Šapirovskii technique to prove three cardinal inequalities. The first two results are due to Fedeli [2] and the third theorem of this paper is a common generalization to: (a) (Arhangel’skii [1]) If X is a T 1 space such that (i) L ( X ) t ( X ) ≤ κ , (ii) ψ ( X ) ≤ 2 κ , and (iii) for all A ∈ [ X ] ≤ 2 κ , A ¯ ≤ 2 κ , then | X | ≤ 2 κ ; and (b) (Fedeli [2]) If X is a T 2 -space then | X | ≤ 2 aql ( X ) t ( X ) ψ c ( X ) .