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

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageUndefined/Unknown
Pages (from-to)61-95
Number of pages35
JournalCommentationes Mathematicae Universitatis Carolinae
Volume60
Issue number1
DOIs
Publication statusPublished - 2019

Keywords

  • Cichoń's diagram
  • Compact cardinal
  • Forcing
  • Set theory of the reals

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