Another ordering of the ten cardinal characteristics in Cichoń's diagram

Kellner, Jakob ; Shelah, Saharon ; Tănasie, Anda R.

Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 1, pp. 61-95.

Résumé

It is consistent that $$ \aleph_1 {\rm add}{(\mathcal N)} {\rm add}{(\mathcal M)}= \mathfrak{b} {\rm cov} {(\mathcal N)} {\rm non}{(\mathcal M)} {\rm cov}{(\mathcal M)} = 2^{\aleph_0}. $$ Assuming four strongly compact cardinals, it is consistent that \begin{align*} \aleph_1 {\rm add}{(\mathcal N)} {\rm add}{(\mathcal M)} =\mathfrak{b} {\rm cov} {(\mathcal N)} {\rm non}{(\mathcal M)} {\rm cov}{(\mathcal M)} {\rm non}{(\mathcal N)} {\rm cof}{(\mathcal M)}= \mathfrak{d} {\rm cof}{(\mathcal N)} 2^{\aleph_0}. \end{align*}

Détail

DOI : 10.14712/1213-7243.2015.273

Classification : 03E17
Keywords: set theory of the reals; Cichoń's diagram; forcing; compact cardinal