Bases and selectors for tall families

2017/10/24 by Grebik, Jan, Uzcategui, Carlos
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1710.08766

Abstract

We show that the Nash-Williams theorem has a uniform version and that the Galvin theorem does not. We show that there is an F_σ tall ideal on ℕ without a Borel selector and also construct a \mathbfΠ¹₂ tall ideal without a tall closed subset.

Related

• Tall F_σ subideals of tall analytic ideals
• No minimal tall Borel ideal in the Katětov order
• Galvin's Conjecture and Weakly Precipitous Ideals
• Rapid ultrafilters and summable ideals
• Nash blowups in prime characteristic