@article{9e2d399534a8465db31bfb9b70679763,
title = "Another ordering of the ten cardinal characteristics in Cicho{\'n}'s diagram",
abstract = "It is consistent that in Cicho{\'n}'s diagram, \$\$ \textbackslash{}aleph\_1 < \{\textbackslash{}rm add\}\{(\textbackslash{}mathcal N)\}< \{\textbackslash{}rm add\}\{(\textbackslash{}mathcal M)\}= \textbackslash{}mathfrak\{b\} < \{\textbackslash{}rm cov\} \{(\textbackslash{}mathcal N)\} < \{\textbackslash{}rm non\}\{(\textbackslash{}mathcal M)\} < \{\textbackslash{}rm cov\}\{(\textbackslash{}mathcal M)\} = 2\textasciicircum{}\{\textbackslash{}aleph\_0\}. \$\$ Assuming four strongly compact cardinals, it is consistent that \textbackslash{}begin\{align*\} \textbackslash{}aleph\_1 \&< \{\textbackslash{}rm add\}\{(\textbackslash{}mathcal N)\} < \{\textbackslash{}rm add\}\{(\textbackslash{}mathcal M)\} =\textbackslash{}mathfrak\{b\} < \{\textbackslash{}rm cov\} \{(\textbackslash{}mathcal N)\} < \{\textbackslash{}rm non\}\{(\textbackslash{}mathcal M)\} \&<\{\textbackslash{}rm cov\}\{(\textbackslash{}mathcal M)\}< \{\textbackslash{}rm non\}\{(\textbackslash{}mathcal N)\} < \{\textbackslash{}rm cof\}\{(\textbackslash{}mathcal M)\}= \textbackslash{}mathfrak\{d\} < \{\textbackslash{}rm cof\}\{(\textbackslash{}mathcal N)\} < 2\textasciicircum{}\{\textbackslash{}aleph\_0\}. \textbackslash{}end\{align*\}. This oaper is an application of Boolean Ultrapowers in set theoretical context. The mentioned consistency results extends the famous set theory paper Cicho{\'n}'s maximum.",
author = "J. Kellner and S. Shelah and A.R. T{\u a}nasie",
year = "2019",
doi = "10.14712/1213-7243.2015.273",
language = "Undefined/Unknown",
journal = "Commentationes Mathematicae Universitatis Carolinae",
issn = "0010-2628",
publisher = "Charles University, Faculty of Mathematics and Physics",
}