Coanalytic Ultrafilter Bases

2019/12/19 by Schilhan, Jonathan · 1 citation
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1912.09138

Abstract

We study the definability of ultrafilter bases on ω in the sense of descriptive set theory. As a main result we show that there is no coanalytic base for a Ramsey ultrafilter, while in L we can construct Π¹₁ P-point and Q-point bases. We also show that the existence of a \mathbfΔ¹_n+1 ultrafilter is equivalent to that of a \mathbfΠ¹_n ultrafilter base, for n ∈ ω. Moreover we introduce a Borel version of the classical ultrafilter number and make some observations.

Cited by

• Coanalytic families of functions

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