5 citations · 7 across the 9 of their papers we have counts for
11 papers
Weak -sets and almost-normal Isbell-Mrówka spaces
César Ismael Corral Rojas, Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim
We determine the least cardinality of a set of reals that is not a weak -set, proving that it is , where and are the…
Existence of bases implies the axiom of choice, a foundation-free proof
Gabriel Fernandes, Renan Maneli Mezabarba, Vinicius de Oliveira Rodrigues
We prove that, in Zermelo--Fraenkel set theory with the axiom of Foundation removed, the statement that every vector space has a basis implies the Axiom of Choice (),…
A Borel Concept Class of VC Dimension One with a Non-PAC Consistent Learner in ZFC
Mateus Jesus de Arruda Campos, Gabriel Fernandes, Vinicius de Oliveira Rodrigues
The fundamental theorem of statistical learning states that, under suitable measurability assumptions, finite Vapnik--Chervonenkis (VC) dimension guarantees that every proper consi…
The Wallace problem and countably compact torsion-free Abelian groups in ZFC
Juliane Trianon Fraga, Vinicius de Oliveira Rodrigues
We prove in ZFC that every torsion-free Abelian group of cardinality admits a Hausdorff countably compact group topology without nontrivial convergent sequences. In p…
Countable compactness in powers of topological groups and Ramsey theoretic variations of compactness
Vinicius de Oliveira Rodrigues, Paul Jan Szeptycki, Artur Hideyuki Tomita
Countable compactness need not be preserved by finite products. Motivated by compactness notions for maps indexed by finite subsets of , we introduce cascade countable compactne…
Determining the Rearrangement Number
Vinicius de Oliveira Rodrigues
The rearrangement number is the least cardinality of a collection of permutations of such that every conditionally convergent real series is disrupted by some p…
Almost Disjointness Principles and -Space Cardinals
Vinicius de Oliveira Rodrigues
Banakh and Bazylevych introduced separation-axiom variants , for , of the cardinal , together with a cardinal lying…
A Wallace semigroup whose every finite power is countably compact
Juan Luis Jaisuño Fuentes-Maguiña, Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita
We show that, assuming the existence of incomparable selective ultrafilters, there exists a Wallace semigroup whose infinite countable power is the least power which…
On Products of -sets
Rodrigo Rey Carvalho, Vinicius de Oliveira Rodrigues
We prove the consistency of the existence of a -set whose square is not a -set and that if there is a -set, then there exists a -set whose all finite powers are -set…
Almost-normality of Isbell-Mrówka spaces
Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim
We explore almost-normality in Isbell-Mrówka spaces and some related concepts. We use forcing to provide an example of an almost-normal not normal almost disjoint family, explore t…
Algebraic structure of countably compact non-torsion Abelian groups of size continuum from selective ultrafilters
M. K. Bellini, A. C. Boero, V. O. Rodrigues +1
Assuming the existence of incomparable selective ultrafilters, we classify the non-torsion Abelian groups of cardinality that admit a countably compact…