A cardinal invariant related to homogeneous families

Details A cardinal invariant related to homogeneous families A cardinal invariant related to homogeneous families

1997-07-16

arxiv.org/abs/math/9707201v1

Mathematics

Logic

This is a draft version; the paper might be expanded in the future. Number E14 on Shelah's E-list.

Scientific paper

Let "ex" be the cardinality of the smallest independent family of subsets of omega (independent means that all nontrivial Boolean combinations are infinite) which cannot be extended to a homogeneous independent family. "Homogeneous" means that every finite partial map (points to points, sets to sets) that is compatible with the family is induced by a permutation of omega. Despite its apparently ``complex'' (second order) definition, this cardinal is equal to a well-known ``simple'' cardinal invariant from Cichon's diagram.

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