arXiv subjects

Vinicius de O. Rodrigues

Publications and source records attributed to Vinicius de O. Rodrigues.

2 recordsLinked to original sources

arXiv2023

New examples of MAD families with pseudocompact hyperspaces

We show that both $\mathfrak{ap=c}$ and $\diamondsuit(\mathfrak{b})$ imply the existence of MAD families with pseudocompact Vietoris hyperspace, substantially expanding the list of models where their existence is known. We also discuss some properties on the structure of fin-intersecting MAD families by providing some new examples of non-fin-intersecting MAD families with special properties. We show that the Baire number of $ω^*$ is strictly larger than $\mathfrak c$ if and only if for every MAD family $\mathcal A$, $Ψ(\mathcal A)$ and its Vietoris hyperspace are $p$-pseudocompact for some free ultrafilter $p$.

math.GN↗

arXiv2023

Fin-intersecting MAD families

We introduce a new class of almost disjoint families which we call fin-intersecting almost disjoint families. They are related to almost disjoint families whose Vietoris Hyperspace of their Isbell-Mrówka spaces are pseudocompact. We show that under $\mathfrak p=\mathfrak c$ fin-intersecting MAD families exist generically and they also exist if $\mathfrak{a<s}$, but that there are also non fin-intersecting MAD families in ZFC. We also show that under CH, there exists fin intersecting MAD families which remain like that after adding an arbitrary quantity of Cohen reals and Random reals. These results give more models in which pseudocompact MAD families exist.

math.GN↗