A parametrized diamond principle and union ultrafilters
Volume 153 / 2018
Colloquium Mathematicum 153 (2018), 261-271
MSC: Primary 03E35; Secondary 03E65, 03E17, 54D80.
DOI: 10.4064/cm7364-10-2017
Published online: 8 June 2018
Abstract
We consider a cardinal invariant closely related to Hindman’s theorem. We prove that this invariant is small in the iterated Sacks perfect set forcing model, and its corresponding parametrized diamond principle implies the existence of union ultrafilters. As a corollary, we obtain the existence of union ultrafilters in the iterated Sacks model of set theory.
