Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We consider a combinatorial problem related to guessing the values of a function at various points based on its values at certain other points, often presented by way of a hat-problem metaphor: there are a number of players who will have colored hats placed on their heads, and they wish to guess the colors of their own hats. A visibility relation specifies who can see which hats. This paper focuses on the existence of minimal predictors: strategies guaranteeing at least one player guesses correctly, regardless of how the hats are colored. We first present some general results, in particular showing that transitive visibility relations admit a minimal predictor exactly when they contain an infinite chain, regardless of the number of colors. In the more interesting nontransitive case, we focus on a particular nontransitive relation on ω that is elementary, yet reveals unexpected phenomena not seen in the transitive case. For this relation, minimal predictors always exist for two colors but never for ℵ₂ colors. For ℵ₀ colors, the existence of minimal predictors is independent of ZFC plus a fixed value of the continuum, and turns out to be closely related to certain cardinal invariants involving meager sets of reals.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
273-285
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- Department of Mathematics, Union College, Schenectady, NY 12308, U.S.A.
autor
- Department of Mathematics, Union College, Schenectady, NY 12308, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-3-4