Ultrafilter with predecessors in Rudin-Frolík order
Lev Bukovský, Eva Butkovičová (1981)
Commentationes Mathematicae Universitatis Carolinae
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Ultrafilter with predecessors in Rudin-Frolík order
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Prediction problems and ultrafilters on ω
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We consider prediction problems in which each of a countably infinite set of agents tries to guess his own hat color based on the colors of the hats worn by the agents he can see, where who can see whom is specified by a graph V on ω. Our interest is in the case in which 𝓤 is an ultrafilter on the set of agents, and we seek conditions on 𝓤 and V ensuring the existence of a strategy such that the set of agents guessing correctly is of 𝓤-measure one. A natural necessary condition is...