4 papers
math.LO2025
Monotonicity of the ultrafilter number function
Toshimichi Usuba
We investigate whether the ultrafilter number function on the cardinals is monotone, that is, whether holds for…
math.LO2025
On Recurrence Axioms
Sakaé Fuchino, Toshimichi Usuba
The Recurrence Axiom for a class of \pos\ and a set of parameters is an axiom scheme in the language of ZFC asserting that if a statement with parameters from …
math.LO2025
Variants of ÅoÅ's Theorem
Toshimichi Usuba
We study ÅoÅ's theorem in a choiceless context. We introduce some variants of ÅoÅ's theorem. These variants seem weaker than ÅoÅ's theorem, but we prove that these are equiva…
math.LO2024
Generically extendible cardinals
Toshimichi Usuba
In this paper, we study the notion of a generically extendible cardinal, which is a generic version of an extendible cardinal. We prove that the generic extendibility of or…