Monadic Sigma(1)(1) and Modal Logic with Quantified Binary Relations

We investigate the expressive power of a range of modal logics extended with second-order prenex quantification of binary and unary relations. Our principal result is that Sigma(1)(1) (BML=), i.e., Boolean modal logic extended with the identity modality and existential prenex quantification of binary and unary relations, translates into monadic Sigma(1)(1). We also briefly discuss a variety of decidability results in multimodal logic implied by our result.