5 papers · 1 filter
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…
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 …
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…
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…
A note on ÅoÅ's Theorem without the Axiom of Choice
Toshimichi Usuba
We study some topics about ÅoÅ's theorem without assuming the Axiom of Choice. We prove that ÅoÅ's fundamental theorem of ultraproducts is equivalent to a weak form that every…