Selective Coideals on (f In

A notion of selective coideal on (FIN [∞] k ,≤) (see definitions below) is given. The natural versions of the local Ramsey property and the abstract Baire property relative to this context are proven to be equivalent, and it is also shown that the family of subsets of FIN [∞] k having the local Ramsey property relative to a selective coideal on (FIN [∞] k ,≤) is closed under the Souslin operation. Finally, it is proven that such selective coideals satisfy a sort of canonical partition property, in the sense of Taylor [16].