文摘
We investigate the question of whether 031087425b1b5072c6581f4a4404" title="Click to view the MathML source">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 0364cb46c3d5fc17f4b9f5fcc7f" title="Click to view the MathML source">d=c, and in the Random real model.