Products of Directed Sets with Calibre $({\omega }_1,\omega )$

Paul Gartside, Jeremiah Morgan

A directed set $P$ is calibre $({\omega }_1,\omega )$ if every uncountable subset of $P$ contains an infinite bounded subset. $P$ is productively calibre $({\omega }_1,\omega )$ if $P\times Q$ is calibre $…