Differences between the uniform diameter two properties

Abstract

We study uniform versions of the diameter two properties, that is, the uniform slice-D2P, the uniform D2P and the uniform SD2P, as the property that every ultrapower over any free ultrafilter over $\mathbb{N}$ has the respective diameter two property. The aim of this note is to prove that all the uniform diameter two properties are different eachother.

arXiv comment21 pages