# Philipp Lücke: Squares, chain conditions, and products

Monday, November 13, 2017, 16.30
Seminar room 0.008, Mathematical Institute, University of Bonn

Speaker: Philipp Lücke (Universität Bonn)

Title: Squares, chain conditions, and products

Abstract:

With the help of square principles, we obtain results concerning the consistency strength of several statements about strong chain conditions and their productivity. In particular, we show that if the κ-Knaster property is countably productive for some uncountable regular cardinal κ, then κ is weakly compact in L. The proof of this result relies on a new construction that shows that Todorcevic’s principle □(κ) implies an indexed version of the principle □(κ,λ). This is joint work with Chris Lambie-Hanson (Bar-Ilan).