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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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