A cardinal invariant related to homogeneous families
Logic
2009-09-25 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/9707201,
title = {A cardinal invariant related to homogeneous families},
author = {Martin Goldstern and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9707201},
year = {2009}
}
Comments
This is a draft version; the paper might be expanded in the future. Number E14 on Shelah's E-list.