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Pseudoradial Spaces: Finite Products and an Example From CH

Simon, PetrTironi, Gino — 1998

Serdica Mathematical Journal

∗ The first named author’s research was partially supported by GAUK grant no. 350, partially by the Italian CNR. Both supports are gratefully acknowledged. The second author was supported by funds of Italian Ministery of University and by funds of the University of Trieste (40% and 60%). Aiming to solve some open problems concerning pseudoradial spaces, we shall present the following: Assuming CH, there are two semiradial spaces without semi-radial product. A new property of pseudoradial spaces...

Sacks forcing collapses 𝔠 to 𝔟

Petr Simon — 1993

Commentationes Mathematicae Universitatis Carolinae

We shall prove that Sacks algebra is nowhere ( 𝔟 , 𝔠 , 𝔠 ) -distributive, which implies that Sacks forcing collapses 𝔠 to 𝔟 .

On the existence of true uniform ultrafilters

Petr Simon — 2004

Commentationes Mathematicae Universitatis Carolinae

We shall show that there is an ultrafilter on singular κ with countable cofinality, which cannot be reached from the set of all subuniform ultrafilters by iterating the closure of sets of size < κ .

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