Important properties include, of course, soundness and completeness, as well as finite model property: if a formula is false in some interpretation, then it is false a finite interpretation.What is important to say about a boolean algebra (or any other semantic)

A Boolean algebra is a partially ordered set. One can build a so-called interval algebra from a totally ordered sets. Yes, Boolean algebras can be infinite.the boolean algebras are defined on finite, totally ordeerd sets; my intuition is that it could be extended for infinite, totally ordered sets

Which class?Also, this particular boolean algebra belongs to a specific class of boolean algebras. What should I mention about this specific class.

Some types and properties of Boolean algebras as mentioned in Wikipedia and the Stanford Encyclopedia of Philosophy.