On the Milner-shelah Condition for Transversals
نویسنده
چکیده
2. An important concept will be that of a component of a family 2F. Consider the equivalence relation on / generated by the relation R defined by: i'RV'o Fv n Fr T* 0 . Let /* be any equivalence class. Then &* = is, by definition, a component of $F. If Fv and Fv> are in different components, then jp., n Fv> = 0 . This means that 0? has a transversal if and only if every component of SF has one, and that $F satisfies (1) if and only if every component does so. Two more definitions are needed to state the lemma below. The length of the family 3F is simply |/|. A regular cardinal X (as opposed to a singular one) is one which cannot equal the sum of < X cardinals, every one of which is < X. Thus, 0,1, 2 and Ko are the 4 smallest regular cardinals.
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