Squares, ascent paths, and chain conditions, part 2

שלחו לחבר
Chris Lambie-Hanson (BIU)
13/11/2017 - 15:00 - 13:00
Building 505, Room 65
We continue our pair of talks on connections between square principles, trees with ascent paths, and strong chain conditions.
In the previous talk, we discussed trees with ascent paths; we turn our attention this week to chain conditions. In particular, we will prove that, if $\kappa > \aleph_1$ is a regular cardinal and $\square(\kappa)$ holds, then:
1) There is a $\kappa$-Knaster poset $\mathbb{P}$ such that $\mathbb{P}^\omega$ is not $\kappa$-c.c.
2) There is a $\kappa$-Knaster poset $\mathbb{P}$ that is not $\kappa$-stationarily layered.
This talk will rely only minimally on material from the previous talk, and the results are joint work with Philipp Lücke.