TITLE: Is $\clubsuit_{\omega_1}$ enough to get Suslin tree?
QUESTION [10 upvotes]: This is problem 15.3 in Arnie Miller's problem list: 
(Juhasz) Suppose there exists $\langle A_{\alpha} : \alpha \in L \rangle$, where $L$ is the set of limit ordinals below $\omega_1$ and for each $\alpha \in L$, $A_{\alpha}$ is an unbounded subset of $\alpha$, satisfying: For every unbounded $A \subseteq \omega_1$, there exists $\alpha \in L$, $A_{\alpha} \subseteq A$. Must there exists a Suslin tree?
What is the current status of this problem? Thanks!

REPLY [10 votes]: The answer is negative apparently. It is consistent relative to ZFC that all Aronszajn trees are
special and that the club principle holds: 
http://home.mathematik.uni-freiburg.de/mildenberger/postings/paperspdf/988_2014_10_15no.pdf