Some results on nonstationry ideal 2

Some remarks on Kuratowski partitions

We introduce the notion of $K$-ideals associated with Kuratowski partitions and we prove that each $κ$-complete ideal on a measurable cardinal $κ$ can be represented as a $K$-ideal. Moreover, we show some results concerning precipitous and Fréchet ideals.

Ideals determined by some Souslin forcing notions

We describe a method of building ``nice'' sigma-ideals from Souslin ccc forcing notions. [These notes were written down in 1992, but were not submitted to any journal. In a slightly modified form, they were incorporated to: T. Bartoszynski and H. Judah, Set Theory: on the structure of the real line, A K Peters, Wellesley, MA, 1995; pages 193-203.]

The null ideal restricted to some non-null set may be $\aleph_1$-saturated

Our main result is that possibly some non-null set of reals cannot be divided to uncountably many non-null sets. We deal also with a non-null set of reals, the graph of any function from it is null and deal with our iterations somewhat more generally.

Consistency of "the ideal of null restricted to some A is kappa-complete not kappa^+-complete, kappa weakly inaccessible and cov(meagre)=aleph_1"

In this note we answer the following question of Grinblat: Is it consistent that for some set X, cov(NULL restriction X)=lambda is a weakly inaccessible cardinal (so X not null of course) while cov(meagre) is small, say it is aleph_1.

某些半选择理想的一些组合性质

Some combinatorial properties of semiselective ideals

本文研究了半选择理想的一些组合性质，证明了在特定假设下半选择理想补集与选择超滤子的关系，并给出了局部Ramsey性质的Ellentuck定理的另一种证明。

Large cardinal ideals

Building on work of Holy, Lücke and Njegomir \cite{MR3913154} on small embedding characterizations of large cardinals, we use some classical results of Baumgartner (see \cite{MR0384553} and \cite{MR0540770}), to give characterizations of several well-known large cardinal ideals, including the Ramsey ideal, in terms of generic elementary embeddings; we also point out some seemingly inherent differences between small embedding and generic embedding characterizations of subtle cardinals. Additionally, we present a simple and uniform proof which shows that, when $κ$ is weakly compact, many large c…