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

Kellner, Jakob, Shelah, Saharon, and Tănasie, Anda R.. "Another ordering of the ten cardinal characteristics in Cichoń's diagram." Commentationes Mathematicae Universitatis Carolinae 60.1 (2019): 61-95. <http://eudml.org/doc/294479>.

@article{Kellner2019,
abstract = {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*\}},
author = {Kellner, Jakob, Shelah, Saharon, Tănasie, Anda R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {set theory of the reals; Cichoń's diagram; forcing; compact cardinal},
language = {eng},
number = {1},
pages = {61-95},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Another ordering of the ten cardinal characteristics in Cichoń's diagram},
url = {http://eudml.org/doc/294479},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Kellner, Jakob
AU - Shelah, Saharon
AU - Tănasie, Anda R.
TI - Another ordering of the ten cardinal characteristics in Cichoń's diagram
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 1
SP - 61
EP - 95
AB - 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*}
LA - eng
KW - set theory of the reals; Cichoń's diagram; forcing; compact cardinal
UR - http://eudml.org/doc/294479
ER -