Hannes Jakob:
Strong distributivity and games on posets
Zeit und Ort
Dienstag, 25.4.23, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Zusammenfassung
A forcing order is said to be \(<\bkappa\)-distributive iff it does not add new sequences of length \(<\bkappa\). A sufficient but not necessary condition for this is that the forcing is \(<\bkappa\)-closed, i.e. any \(<\bkappa\)-sequence of conditions has a lower bound. We introduce a strenghtening of \(<\bkappa\)-distributivity called strong \(<\bkappa\)-distributivity which can replace \(<\bkappa\)-closure in many applications. A main benefit of this property is that a \(<\bkappa\)-closed forcing remains strongly \(<\bkappa\)-distributive in any extension by a \(\bkappa\)-cc. order, even though it no longer necessarily is \(<\bkappa\)-closed.