Local operations and eventually open actions

Hydra games for recursively Mahlo operations

A hydra game is proposed, and the fact that every hydra eventually die out is shown to be equivalent (over a weak arithmetic) to the 1-consistency of set theory KPM for recursively Mahlo universes.

关于星运算和Baire空间上的一些理想

On Star operation and some ideals on the Baire space

本文研究了Baire空间上的几个σ-理想，引入并分析了理想G和SMZ⁺，建立了它们与经典理想的结构关系，计算了M₋的基数不变量，并证明了星运算下的对偶关系，最后证明了M₋的树二分定理。

A topological semigroup structure on the space of actions modulo weak equivalence

We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous operation with respect to this topology, so that the space of actions modulo weak equivalence becomes a topological semigroup.