# Definition Let $(T,<)$ be a [[Trees#^suslin|Suslin tree]], and let $(P_{T},<)=(T,>)$ i.e. $T$ with the reverse order # Properties - [[Chain conditions#^ccc|ccc]] - $\aleph_{0}$-[[Distributivity|distributive]] if $T$ is [[Trees#^normal|normal]]. - If $T$ is a normal Suslin tree then $P_T \times P_T$ does not satisfy the countable chain condition. - On the other hand, if $T,S$ are (normal) Suslin trees, then $T \times S$ (tree product) is Suslin iff $P_{T} \Vdash S$ is Suslin iff $P_{S} \Vdash T$ is Suslin. (see [[Chain conditions#^eaac13|here]])