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Sittinon Jirattikansakul

Publications and source records attributed to Sittinon Jirattikansakul.

7 recordsLinked to original sources
arXiv2026

Congruences via Partitions with Exactly Two Part Sizes

We prove the congruence $\sum_{1 \leq k < \sqrt{N}} σ_0 (N - k^2) \equiv 0 \pmod 4$, where $σ_0(m)$ denotes the number of positive divisors of $m$, for $N = An + B$ with $(A,B) \in \{ (16,14),$ $(36,30),$ $(72,42),$ $(196,70),$ $(252,114) \}$. Our proof relies on a result of Keith which states that $ν_2 (N) \equiv 0 \pmod 4$, where $ν_2(N)$ is the number of partitions of $N$ with exactly two part sizes. Inspired by Dewitt and Keith, our approach combines combinatorial arguments with modular arithmetic techniques.

math.NT↗
arXiv2025

A model for global compactness

In a classical paper by Ben-David and Magidor, a model of set theory was exhibited in which $\aleph_{ω+1}$ carries a uniform ultrafilter that is $θ$-indecomposable for every uncountable cardinal $θ<\aleph_ω$. In this paper, we give a global version of this result, as follows: Assuming the consistency of a supercompact cardinal, we produce a model of set theory in which for every singular cardinal $λ$, there exists a uniform ultrafilter on $λ^+$ that is $θ$-indecomposable for every cardinal $θ$ such that $cf(λ)<θ<λ$. In our model, many instances of compactness for chromatic numbers hold, from which we infer that Hajnal's gap-1 counterexample to Hedetniemi's conjecture is best possible on the grounds of ZFC.

math.LO↗
arXiv2025

A Small Ultrafilter Number at Every Singular Cardinal

We obtain a small ultrafilter number at $\aleph_{ω_1}$. Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal $κ$ inaccessible. We apply this forcing to construct a model where $κ$ is the least inaccessible and $V_κ$ is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers at all singulars are small.

math.LO↗
arXiv2023

Extender-based Magidor-Radin forcings without top extenders

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 approach to obtain a failure of SCH on a club subset of an inaccessible cardinal, and a model where the cardinal arithmetic behaviors are different on stationary classes, whose union is the club, is provided. The cardinals and the cofinalities outside the clubs are not affected by the forcings.

math.LO↗
arXiv2022

Blowing up the power of a singular cardinal of uncountable cofinality with collapses

The {\em Singular Cardinal Hypothesis} (SCH) is one of the most classical combinatorial principles in set theory. It says that if $κ$ is singular strong limit, then $2^κ=κ^+$. We prove that given a singular cardinal $κ$ of {\em cofinality} $η$ in the ground model, which is a limit of suitable large cardinals, and $η^+=\aleph_γ$, then there is a forcing extension which preserves cardinals and cofinalities up to and including $η$, such that $κ$ becomes $\aleph_{γ+η}$, and SCH fails at $κ$. Furthermore, if $η$ is not an $\aleph$-fixed point, then in our model, SCH fails at $\aleph_η$. Our large cardinal assumption is below the existence of a Woodin cardinal. In our model we also obtain a very good scale.

math.LO↗
arXiv2021

Forcing with overlapping supercompact extenders

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 supercompact cardinals, it is possible to force so that the size of the powerset of the singular cardinal is arbitrarily large, while preserving the singular cardinal. An important feature of this forcing is that it is possible to define the forcing so that the successor of the singular cardinal is collapsed, but all the cardinals above it are preserved.

math.LO↗