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A parametrized diamond principle and union ultrafilters

Volume 153 / 2018

David Fernández-Bretón, Michael Hrušák Colloquium Mathematicum 153 (2018), 261-271 MSC: Primary 03E35; Secondary 03E65, 03E17, 54D80. DOI: 10.4064/cm7364-10-2017 Published online: 8 June 2018


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.


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