Jiachen Yuan (Leeds)

Weak Threads for Ladder Systems at Inaccessible $\kappa$

"Every club sequence has a weak thread" is a compactness property that implies simutaneously stationary reflection. In this talk, we will first explore weak threads for various ladder systems. Then we show it is consistent that every club sequence has a weak thread and there exists an almost disjoint ladder system given by vanishing branches of a $\kappa$-Suslin tree. This is joint work with Assaf Rinot and Zhixing You.