Cardinal characteristics at $$\aleph_\omega$$
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-019-00971-0
Abstract: We prove the consistency of $$\mathfrak{u}_{\aleph_\omega} < 2^{\aleph_\omega}$$. We also show that the consistency strength of this statement is the existence of a measurable cardinal $$\kappa$$ with $$o(\kappa) = \kappa^{++}$$ . read more here.
Keywords: cardinal characteristics; kappa; characteristics aleph; aleph omega ... See more keywords
A friendly iteration forcing that the four cardinal characteristics of $\mathcal E$ can be pairwise different
Sign Up to like & getrecommendations! Published in 2022 at "Colloquium Mathematicum"
DOI: 10.4064/cm8917-2-2023
Abstract: Let $\mathcal{E}$ be the $\sigma$-ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\mathcal{E}$, their associated cardinal characteristics (i.e.\ additivity, covering,… read more here.
Keywords: friendly iteration; cardinal characteristics; pairwise different; iteration forcing ... See more keywords