Gruff超滤器
Gruff Ultrafilters
摘要：
我们调查的问题，是否$\mathbb Q$进行完美集产生的超滤子（这种超滤子被称为粗糙超滤范杜文）。我们证明，一个可以（一贯）得到一个肯定的答案，这个问题在三种不同的方式：通过假设一定的参数化钻石原则，从基数不变的平等$\mathfrak d=\mathfrak c$，并在随机真实模型。[Edit：将“Randor实数模型”替换为“通过将$ω_1$ Cohen实数添加到$\mathsf{CH}$的模型中，然后用Random代数进行强制而获得的模型”;这在论文末尾所附的勘误中得到了澄清。]
英文摘要：
We investigate the question of whether $\mathbb Q$ carries an ultrafilter generated by perfect sets (such ultrafilters were called gruff ultrafilters by van Douwen). We prove that one can (consistently) obtain an affirmative answer to this question in three different ways: by assuming a certain parametrized diamond principle, from the cardinal invariant equality $\mathfrak d=\mathfrak c$, and in the Random real model. [Edit: replace "the Randor real model" with "the model obtained by adding $ω_1$ Cohen reals to a model of $\mathsf{CH}$, and subsequently forcing with the Random algebra"; this is clarified in the corrigendum attached at the end of the paper.]
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
