I do not understand the definition of a centered family in a Boolean algebra. Here's the definition
A family $R\subset A$ is said to be centered, if for every finite set $\{a_1,\ldots, a_n\}\subset R$, $a_1,\ldots,a_n > \mathbb{O}$.
this is from Logic of Mathematics by Adamowicz and Zbierski. Part of Exercise 3.9 on page 23. I cannot do the exercise because I don't understand the definition.
Is it saying, "For every finite set $S$, it is the case that $S\subset R$" or is it saying, "For every finite subset $S$ of $R$, all of its elements are positive"? But in a Boolean algebra every element is greater than $\mathbb{O}$.
This appears to be a typo. It should instead say that the meet $a_1\wedge \dots\wedge a_n$ of $a_1,\dots,a_n$ is greater than $0$.