TY - JOUR
T1 - Another ordering of the ten cardinal characteristics in Cichoń's diagram
AU - Kellner, J.
AU - Shelah, S.
AU - Tănasie, A.R.
PY - 2019
Y1 - 2019
N2 - It is consistent that in Cichoń's diagram, $$ \aleph_1 < {\rm add}{(\mathcal N)}< {\rm add}{(\mathcal M)}= \mathfrak{b} < {\rm cov} {(\mathcal N)} < {\rm non}{(\mathcal M)} < {\rm cov}{(\mathcal M)} = 2^{\aleph_0}. $$ 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*}. This oaper is an application of Boolean Ultrapowers in set theoretical context. The mentioned consistency results extends the famous set theory paper Cichoń's maximum.
AB - It is consistent that in Cichoń's diagram, $$ \aleph_1 < {\rm add}{(\mathcal N)}< {\rm add}{(\mathcal M)}= \mathfrak{b} < {\rm cov} {(\mathcal N)} < {\rm non}{(\mathcal M)} < {\rm cov}{(\mathcal M)} = 2^{\aleph_0}. $$ 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*}. This oaper is an application of Boolean Ultrapowers in set theoretical context. The mentioned consistency results extends the famous set theory paper Cichoń's maximum.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85064628650&partnerID=MN8TOARS
U2 - 10.14712/1213-7243.2015.273
DO - 10.14712/1213-7243.2015.273
M3 - Article
SN - 0010-2628
JO - Commentationes Mathematicae Universitatis Carolinae
JF - Commentationes Mathematicae Universitatis Carolinae
ER -