Properties D and aD are different

可数集上的钻石原则与 Tukey-top 超滤

Diamond principles and Tukey-top ultrafilters on a countable set

本文在 ZFC 中构造了满足两类钻石猜测原则的 Tukey-top 超滤，证明完全猜测不可能且不存在 Dodd-sound 超滤，并利用这些原则构造 Tukey-top 的 q-点、证明相关超滤类在 Fubini 和下封闭，同时分离了两类猜测原则。

一种由钻石原理构造的广泛连通拓扑空间

A widely connected topological space made from diamond

本研究利用Jensen的钻石原理$\u2666$构造了一个兼具正则、可分、连通性，且移除任意非空开集后剩余部分完全不连通，同时满足强Choquet性质的特殊无限拓扑空间。

On large sequential groups

We construct, using $\diamondsuit$, an example of a sequential group $G$ such that the only countable sequential subgroups of $G$ are closed and discrete, and the only quotients of $G$ that have a countable pseudocharacter are countable and Fréchet. We also show how to construct such a $G$ with several additional properties (such as make $G^2$ sequential, and arrange for every sequential subgroup of $G$ to be closed and contain a nonmetrizable compact subspace, etc.). Several results about $k_ω$ sequential groups are proved. In particular, we show that each such group is either locally compact…

Notes on linearly H-closed spaces and od-selection principles

A space is called linearly H-closed iff any chain cover possesses a dense member. This property lies strictly between feeble compactness and H-closedness. While regular H-closed spaces are compact, there are linearly H-closed spaces which are even collectionwise normal and Fréchet-Urysohn. We give examples in other classes, and ask whether there is a first countable normal linearly H-closed non-compact space in ZFC. We show that PFA implies a negative answer if the space is moreover either locally separable or locally compact and locally ccc. Ostaszewski space (built with $\diamondsuit$) is an…

具有不可分测度的可数紧对偶球

Countably tight dual ball with a nonseparable measure

本文在钻石原理假设下构造了一个紧空间K，使得P(K)可数紧但K上存在不可数Maharam型的Radon测度，从而区分了P(K×K)与P(K)×P(K)的紧性并回答了Pol的问题。