Are the terms 'clan' and 'tribe' common in mathematics? In the book _'Vector Measures'_ by Dinculeanu, he starts the discussion by talking about "classes of sets", and introduces two pieces of terminology I've never seen before, and can't find any evidence of being used elsewhere. > A nonvoid class $\mathcal{C}$ of subsets of T is called a _clan_ if > > * $A-B\in\mathcal{C}$, for $A,B\in \mathcal{C}$ > > * $A\cup B\in \mathcal{C}$, for $A,B\in \mathcal{C}$ > > And > A nonvoid class $\mathcal{T}$ of subsets of T is called a _tribe_ if > > * $A-B\in\mathcal{C}$, for $A,B\in \mathcal{C}$ > > * $\cup^\infty_{i=1}A_i\in\mathcal{T}$ for every sequence $(A_i)$ of sets of $\mathcal{T}$ > > Now he does make a footnote that "clan" is also called a "ring, by Halmos", and that "tribe" is called (also by Halmos) a "$\sigma$-ring". But I'm curious, why these new, odd terms? And are they used elsewhere commonly at all? Sorry, btw, of my latex is messed up. I'm on mobile.

They are not new terms. They are terms originally used in French. Even today we find some texts in French using those terms, although "ring" and "$\sigma$-ring" have became kind of international standard.