A note on ultrafilters on Boolean algebras

Igor Protasov, Serhii Slobodianiuk

Анотація


Under some conditions on the action of a semigroup $S$ on a Boolean algebra $B$, we consider the natural action of $S$ on the Stone space $Ult(B)$ of $B$ and characterize minimal closed $S$-invariant subsets of $Ult(B)$. As a corollary, we get: if $1_B=a_1\vee\dots\vee a_n$ then some element $a_i$ is relatively large with respect to the action of $S$.

Ключові слова


ultrafilter, action, semigroup, large set, prethick set

Посилання


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