In this paper we investigate several extensions of the first order-language with finitely many binary relations. The most interesting of the studied extensions appears to be the monadic second-order one. We show that the extended languages have the same expressive power as the first-order language over the class of all relational structures of equivalence relations in local agreement by providing appropriate translation of formulae. The decidability of the considered extensions over the above mentioned class of structures is also shown.

Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.