O. Guzmán

collaborators

5 papers

math.GN2020

Maximal almost disjoint families and pseudocompactness of hyperspaces

Osvaldo Guzmán, Michael Hrušák, Vinicius de Oliveira Rodrigues +2

We show that all maximal almost disjoint families have pseudocompact Vietoris hyperspace if and only if $MA_{c} (P (ω) / fin)$ holds. We further stu…

math.LO2019

Splitting chains, tunnels and twisted sums

Félix Cabello Sánchez, Antonio Avilés, Piotr Borodulin-Nadzieja +2

We study splitting chains in $P (ω)$ , that is, families of subsets of $ω$ which are linearly ordered by $\subseteq^{*}$ and which are splitting. We prove that their existenc…

math.LO2018

P-points, MAD families and Cardinal Invariants

Osvaldo Guzman

This is the Ph.D. thesis of the author, which was written under the supervision of Michael Hrušák at UNAM. The main contributions of this thesis are the following: There is a $+$ -R…

math.LO2018

On $(1, ω_{1})$ \emph{-}weakly universal functions

Osvaldo Guzman

A function $U : [ω_{1}]^{2} ⟶ ω$ is called $(1, ω_{1})$ \emph{-weakly universal }if for every function $F:\left[ ω_{1}\right] ^{2}\longrightarrowω…

math.LO2018

There is a $+$ -Ramsey \textsf{MAD} family

Osvaldo Guzman

We answer an old question of Michael Hrušák by constructing a $+$ -Ramsey \textsf{MAD} family without the need of any additional axioms beyond $ZFC.$ We also prove that eve…

Maximal almost disjoint families and pseudocompactness of hyperspaces

Splitting chains, tunnels and twisted sums

P-points, MAD families and Cardinal Invariants

On (1,ω1​)\emph{-}weakly universal functions

There is a +-Ramsey \textsf{MAD} family

On $(1, ω_{1})$ \emph{-}weakly universal functions

There is a $+$ -Ramsey \textsf{MAD} family