Incomparable families and maximal trees
Tom 234 / 2016
Fundamenta Mathematicae 234 (2016), 73-89
MSC: 03E17, 03E35, 03G05.
DOI: 10.4064/fm125-1-2016
Opublikowany online: 20 January 2016
Streszczenie
We answer several questions of D. Monk by showing that every maximal family of pairwise incomparable elements of has size continuum, while it is consistent with the negation of the Continuum Hypothesis that there are maximal subtrees of both \mathcal P(\omega ) and \mathcal P(\omega )/\mathit {fin} of size \omega _1.
