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*}
Keywords: set theory of the reals; Cicho\'n's diagram; forcing; compact cardinal
DOI: DOI 10.14712/1213-7243.2015.273
AMS Subject Classification: 03E17