2026/05/31 by Aleksander Cieślak
Mathematics · #math.LO #msc:03E17 #msc:03E05 #msc:03E15
arxiv created 2026/08/01 · arxiv updated 2026/08/04
In this article, we study combinatorial properties of a certain ideal on ω, called the Splitting ideal. We calculate its cardinal invariants and its position in the Katětov order among other definable ideals. We also study the antichain numbers \mathfraka(J) of algebras P(ω)/J for various Borel ideals. We show that \textrmmin\\mathfrakb,\textrmcov+h(J)\≤\mathfraka(J) holds for a wide class of ideals, including all Fσ-ideals, all analytic P-ideals and many other examples. We also show that \mathfrakb≤\mathfraka(J) holds for convergent ideal and for Boring ideal. Finally, we will show the consistency of \mathfraka(J)<\mathfrakb for the Van der Waerden's ideal and the linear growth ideal