[Settfa] Tuesday 04/02, Jakub Andruszkiewicz
kubis at math.cas.cz
kubis at math.cas.cz
Fri Jan 31 20:00:01 CET 2020
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Tuesday 4th February, 10:00am
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Speaker:Jakub Andruszkiewicz, IM CAS / University of Warsaw
Title: On some generalizations of club-like principles
Abstract
We will study generalizations of the ? ( the club principle ) and
of the q ( the stick principle ), including analogous principles on cardinals
other than ? 1 . We will also introduce a notion of the ¶ ( calling it the halfclub
principle ), stating that there exists an q-like almost disjoint family. This
principle is closely related to existence of some instance of the Ciesielski-Pol
compacta. It will be proved, that given appropriate variant of the ¶, we
can extend it on larger cardinals using some particular instances of the ?,
similarly to extending the ? to the ?(? 2 ), done in The Long Club (?) by
Juhász, Nagy, Soukup and Szentmiklóssy. Furthermore, we will generalize
the result of Truss, namely we will prove, that some instance of the q on any
? implies min{cov(N ), cov(M )} ? ?.
(See also the attached pdf file.)
For more information see the seminar web page at
https://calendar.math.cas.cz/set-theory-and-analysis-actual .
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