Generic existence of ultrafilters on the natural numbers
Volume 236 / 2017
Fundamenta Mathematicae 236 (2017), 201-245
MSC: Primary 03E17; Secondary 03E15, 03E35, 03E50.
DOI: 10.4064/fm730-5-2016
Published online: 24 November 2016
Abstract
Say that a class of ultrafilters exists generically if every filter base of size $ \lt {\mathfrak c}$ can be extended to an ultrafilter in that class. We investigate generic existence of ultrafilters defined in terms of ideals on the natural numbers, like the summable ultrafilters and the density zero ultrafilters.
