Abstract
We investigate basic properties of three cardinal invariants involving ω1: stick, antichain number, and matching number. The antichain number is the least cardinal κ for which there does not exist a subcollection of size κ of uncountable subsets of ω1 with pairwise finite intersections and the matching number is the least cardinal κ for which there exists a subcollection X of size κ of order-type ω subsets of ω1 so that every uncountable subset of ω1 has infinite intersection with a member of X. We demonstrate how these numbers are affected by Cohen forcing and also prove some results about the effect of Hechler forcing. We also introduce a forcing notion to increase the matching number, and study its basic properties.
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