Long chains in the Rudin-Frolík order for uncountable cardinals

2023/03/24 by Klaas Pieter Hart, Hart, Klaas Pieter
Mathematics · Computer Science · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.2303.14252

Abstract

We point out that a construction by Butkovičová of a chain of length \mathfrakc⁺ in the Rudin-Frolík order on βω can easily be adapted to produce, given an uncountable cardinal κ, a chain of length (2^κ)⁺ in the Rudin-Frolík order on βκ.

Related

• Chains in Rudin-Frolik order for regulars
• Decreasing chains without lower bounds in Rudin-Frolík order for regulars
• Ultrafilters without immediate predecessors in Rudin-Frolik order for regulars
• A long chain of P-points
• A note on special subsets of the Rudin-Frolík order for regulars