I'm embarrassed to be asking, but: "Write down a set of axioms for the theory of atomless Boolean algebras."
This is Exercise 1.14 in Chapter 9 of "Models and Ultraproducts" by Bell and Slomson. I'm trying to read this on my own. I have no math community except this one.
Clearly we need the axioms for Boolean algebras, and then at least one more. The additional one might say something like: For any non-zero element x, there's a non-zero element y such that 0 < y < x.
But I don't know if that's anywhere close to correct. My further problem is that even if it were, I wouldn't know how to prove I had an axiom system for atomless Boolean algebras. Thanks for any help.
"Clueless in Tucson"