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 language | Undefined/Unknown |
|---|---|
| Pages (from-to) | 61-95 |
| Number of pages | 35 |
| Journal | Commentationes Mathematicae Universitatis Carolinae |
| Volume | 60 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2019 |
Keywords
- Cichoń's diagram
- Compact cardinal
- Forcing
- Set theory of the reals
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