Displaying similar documents to “Two cases when d κ and d * κ are equal”

On the bounding, splitting, and distributivity numbers

Alan S. Dow, Saharon Shelah (2023)

Commentationes Mathematicae Universitatis Carolinae

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The cardinal invariants 𝔥 , 𝔟 , 𝔰 of 𝒫 ( ω ) are known to satisfy that ω 1 𝔥 min { 𝔟 , 𝔰 } . We prove that all inequalities can be strict. We also introduce a new upper bound for 𝔥 and show that it can be less than 𝔰 . The key method is to utilize finite support matrix iterations of ccc posets following paper Ultrafilters with small generating sets by A. Blass and S. Shelah (1989).

Reflecting character and pseudocharacter

Lucia R. Junqueira, Alberto M. E. Levi (2015)

Commentationes Mathematicae Universitatis Carolinae

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We say that a cardinal function φ reflects an infinite cardinal κ , if given a topological space X with φ ( X ) κ , there exists Y [ X ] κ with φ ( Y ) κ . We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences...

A partition property of cardinal numbers

N. H. Williams

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CONTENTSIntroduction....................................................................................... 5§ 1. Notation and definitions......................................................... 5§ 2. Negative relations.................................................................... 9§ 3. The Ramification Lemma ..................................................... 10§ 4. The main theorem................................................................... 13§ 5. A result for cardinals...

On C * -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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