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Incomparable families and maximal trees

G. Campero-Arena; J. Cancino; M. Hrušák; F. E. Miranda-Perea — 2016

Fundamenta Mathematicae

We answer several questions of D. Monk by showing that every maximal family of pairwise incomparable elements of 𝒫(ω)/fin has size continuum, while it is consistent with the negation of the Continuum Hypothesis that there are maximal subtrees of both 𝒫(ω) and 𝒫(ω)/fin of size ω₁.

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