= Knaster forcing preserves Suslin trees
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If $T$ is a normal splitting <Suslin tree> and $P$ is Knaster, then $P\times T$ is <CCC>, so $P$ forces that the ground tree is still <CCC> Countable levels and splitting persist. A new <cofinal branch> would give an uncountable antichain by splitting, so none is added. This permits adding many Cohen reals while retaining a Suslin tree, and distinguishes Knaster preservation from an unjustified preservation claim for every <CCC> <forcing>.
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