Long chains in the Rudin-Frolík order for uncountable cardinals

Klaas Pieter Hart

Published 2023-03-24Version 1

We point out that a construction by Butkovi\v{c}ov\'a of a chain of length $\mathfrak{c}^+$ in the Rudin-Frol\'ik order on $\beta\omega$ can easily be adapted to produce, given an uncountable cardinal $\kappa$, a chain of length $(2^\kappa)^+$ in the Rudin-Frol\'ik order on $\beta\kappa$.