Covering $^\omega \omega $ by special Cantor sets

Gary Gruenhage; Ronnie Levy

Displaying similar documents to “Covering $^{ω} ω$ by special Cantor sets”

Covering $^{ω} ω$ by special Cantor sets.

Gruenhage, Gary, Levy, Ronnie (2004)

Commentationes Mathematicae Universitatis Carolinae

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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 $\geq ω^{2}$ 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 $ℐ \subset 𝒫 (I)$ is the set of all regular cardinals $κ$ such that there is an increasing chain ${A_{α} : α < κ} \subset ℐ$ with $⋃_{α < κ} A_{α} \notin ℐ$ . 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...

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

Covering ω ω by special Cantor sets.

On ω 2 -saturated families

Pcf theory and cardinal invariants of the reals

Displaying similar documents to “Covering $^{ω} ω$ by special Cantor sets”

Covering $^{ω} ω$ by special Cantor sets.

On $ω^{2}$ -saturated families