Incomparable families and maximal trees

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

doi:10.4064/fm125-1-2016

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Incomparable families and maximal trees

G. Campero-Arena ¹ ; J. Cancino ² ; M. Hrušák ³ ; F. E. Miranda-Perea ¹

¹ Facultad de Ciencias Universidad Nacional Autónoma de México Ciudad Universitaria 04510, México, D.F., Mexico
² Centro de Ciencias Matemáticas Universidad Nacional Autónoma de México A.P. 61-3, Xangari Morelia, Michoacán, Mexico
³ Instituto de Matemáticas Universidad Nacional Autónoma de México Área de la Investigación Científica Circuito exterior, Ciudad Universitaria 04510, México, D.F., Mexico <a href="http://www.matmor.unam.mx/~michael">http://www.matmor.unam.mx/~michael</a>

Fundamenta Mathematicae, Tome 234 (2016) no. 1, pp. 73-89.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

We answer several questions of D. Monk by showing that every maximal family of pairwise incomparable elements of $\mathcal P(\omega )/\mathit {fin}$ 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 $\omega _1$.

DOI : 10.4064/fm125-1-2016

Keywords: answer several questions monk showing every maximal family pairwise incomparable elements mathcal omega mathit fin has size continuum while consistent negation continuum hypothesis there maximal subtrees mathcal omega mathcal omega mathit fin size omega

Affiliations des auteurs :

G. Campero-Arena ¹ ; J. Cancino ² ; M. Hrušák ³ ; F. E. Miranda-Perea ¹

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G. Campero-Arena; J. Cancino; M. Hrušák; F. E. Miranda-Perea. Incomparable families and maximal trees. Fundamenta Mathematicae, Tome 234 (2016) no. 1, pp. 73-89. doi : 10.4064/fm125-1-2016. http://geodesic.mathdoc.fr/articles/10.4064/fm125-1-2016/

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