We give a completeness theorem for a logic with probability quantifiers which is equivalent to the logics described in a recent survey paper of Keisler [K]. This result improves on the completeness ...

We show that two abelian-by-finite groups are elementarily equivalent if and only if they satisfy the same sentences with two alternations of quantifiers. We also prove that abelian-by-finite groups ...

By incorporating unary operations analogous to universal and existential quantifiers, monadic structures offer a refined algebraic framework to capture predicate logics, including those with ...