We say that a poset $P$ has the Knaster property (or is Knaster) if every uncountable subset of $P$ contains an uncountable subset of pairwise compatible conditions.
Let $K$ denote the statement "every c.c.c. poset is Knaster" and let $P$ denote the statement "the product of $2$ c.c.c. posets is c.c.c.". Then we have $\mathsf{MA}_{\aleph_1}\implies K \implies P$.
What are good examples of models showing that the implications are not reversible? (or are they?)
This question was reposted on MO