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- W1639933622 abstract "A system of uniform families on an infinite subset M of N is a collection (A�)�<!1 of families of finite subsets of N (where, Ak consists of all k-element subset of M, for k ∈ N) with the properties that each Ais thin (i.e. it does not contain proper initial segments of any of its element) and the Cantor-Bendixson index, defined for A�, is equal to ξ + 1 and stable when we restrict ourselves to any subset of M. We indicate how to extend the generalized Schreier families to a system of uniform families. Using that notion we establish the correct (countable) ordinal index generalization of the classical Ramsey theorem (which corresponds to the finite ordinal indices). Indeed, for a family F of finite subsets of N, we obtain the following:" @default.
- W1639933622 created "2016-06-24" @default.
- W1639933622 creator A5079074685 @default.
- W1639933622 date "1998-04-14" @default.
- W1639933622 modified "2023-09-27" @default.
- W1639933622 title "Ramsey dichotomies with ordinal index" @default.
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- W1639933622 hasPublicationYear "1998" @default.
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