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-compact group topologies without convergent sequences on countably cofinal torsion-free Abelian groups
Matheus Koveroff Bellini, Artur Hideyuki Tomita
We obtain a forcing construction that shows that it is consistent that the torsion-free Abelian group admits a Hausdorff group topology which is also $\mathcal{U…
Forcing a classification of non-torsion Abelian groups of size at most with non-trivial convergent sequences
Matheus Koveroff Bellini, Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita
We force a classification of all the Abelian groups of cardinality at most that admit a countably compact group with a non-trivial convergent sequence. In particula…
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…
On -compact group topologies on direct sums of
Matheus Koveroff Bellini, Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita
We prove that if is a selective ultrafilter then has a -compact group topology without non-trivial convergent sequences, for each infinite cardinal $κ=κ^…
Countably compact group topologies on non-torsion abelian groups of size continuum with non-trivial convergent sequences
{Matheus Koveroff Bellini, Ana Carolina Boero, Irene Castro Pereira +2
Under , we answer Question 24 of \cite{dikranjan&shakhmatov3} for cardinality , by showing that if a non-torsion Abelian group of size…