7 papers
Congruences via Partitions with Exactly Two Part Sizes
Sittinon Jirattikansakul, Teeradej Kittipassorn, Kraiwich Kongsiri +2
We prove the congruence , where denotes the number of positive divisors of , for with $(A,B) \in…
A model for global compactness
Sittinon Jirattikansakul, Inbar Oren, Assaf Rinot
In a classical paper by Ben-David and Magidor, a model of set theory was exhibited in which carries a uniform ultrafilter that is -indecomposable for every uncoun…
Extender-based Magidor-Radin forcings without top extenders
Moti Gitik, Sittinon Jirattikansakul
Continuing \cite{GitJir22}, we develop a version of Extender-based Magidor-Radin forcing where there are no extenders on the top ordinal. As an application, we provide another appr…
A Small Ultrafilter Number at Every Singular Cardinal
Tom Benhamou, Sittinon Jirattikansakul
We obtain a small ultrafilter number at . Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal …
Another method to add a closed unbounded set of former regulars
Moti Gitik, Sittinon Jirattikansakul
A club consisting of former regulars is added to an inaccessible cardinal, without changing cofinalities outside it. The initial assumption is optimal. A variation of the Radin for…
Forcing with overlapping supercompact extenders
Sittinon Jirattikansakul
We build a supercompact version of the forcing defined in \cite{gitik2019}. For each singular cardinal in the ground model with any fixed cofinality, which is a limit of supercompa…
Blowing up the power of a singular cardinal of uncountable cofinality with collapses
Sittinon Jirattikansakul
The {\em Singular Cardinal Hypothesis} (SCH) is one of the most classical combinatorial principles in set theory. It says that if is singular strong limit, then . We p…