arXiv subjects

Ulises Ariet Ramos-García

Publications and source records attributed to Ulises Ariet Ramos-García.

4 recordsLinked to original sources

arXiv2026

$\mathbb Z$-Ramsey ultrafilters

We study $\mathbb{Z}$-Ramsey ultrafilters, ultrafilters containing witnesses to every shift-invariant instance of Ramsey's theorem. We prove that it is consistent that there are no $\mathbb Z$-Ramsey ultrafilters. We also prove that every $(\mathbb{Z},3)$-Ramsey ultrafilter, as well as every $\mathbb{Z}$-Ramsey P-point, is selective. Further, we exhibit a generic extension -- using quotient algebras of the form $\mathcal{P}(\mathbb{Z})/\mathcal{I}$ for certain $F_{σ}$-ideals -- that contains P-points that are not $\mathbb{Z}$-Ramsey ultrafilters, thereby addressing open questions raised by Petrenko and Protasov.

math.LO↗

arXiv2025

Every Polish group has a non-trivial topological group automorphism

We prove that every Polish group with more than two elements admits a non-trivial topological group automorphism. As a consequence, a hypothetical uniquely homogeneous Polish space with more than two points cannot be a semitopological group.

math.LO↗

arXiv2022

$\mathsf{SOCA}$ and $\mathsf{OGA}$ for $\mathsf{HL}$ spaces with strong properties

We study open colorings in certain classes of hereditary Lindelöf ($\mathsf{HL}$) spaces and submetrizable spaces. In particular, we show that the definible version for the Open Graph Axiom ($\mathsf{OGA}$) holds for the class of $\mathsf{HL}$ strong Choquet submetrizable spaces extending a well-known result of Feng. Furthermore, we show the consistency of the Open Graph Axiom for regular spaces that have countable spread and it's square also has it, reaching closer to a well known conjecture of Todorčević: "It is consistent that all regular spaces with countable spread satisfy $\mathsf{OGA}$".

math.GN↗

arXiv2020

Countably compact groups without non-trivial convergent sequences

We construct, in $\mathsf{ZFC}$, a countably compact subgroup of $2^{\mathfrak{c}}$ without non-trivial convergent sequences, answering an old problem of van Douwen. As a consequence we also prove the existence of two countably compact groups $\mathbb{G}_{0}$ and $\mathbb{G}_{1}$ such that the product $\mathbb{G}_{0} \times \mathbb{G}_{1}$ is not countably compact, thus answering a classical problem of Comfort.

math.GN↗