We prove that for $n=2$ and $n=3$ there is a forcing extension with exactly n near-coherence classes of non-principal ultrafilters. We introduce localized versions of Matet forcing and we develop Ramsey spaces of names. The evaluation of some of the new forcings is based on a relative of Hindman’s theorem due to Blass 1987.

中文翻译：

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恰好两个和恰好三个近相干类

我们证明对于$n=2$和$n=3$存在一个具有恰好n 个近相干类别的非主超滤器的强制扩展。我们引入了 Matet 强迫的本地化版本，并开发了 Ramsey 名称空间。一些新强迫的评估是基于 Blass 1987 的 Hindman 定理的相关定理。