Second-order logic on equivalence relations

Journal of Applied Non-Classical Logics 18 (2-3):229-246 (2008)
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Abstract

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.

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Modal Logic and Classical Logic.Johan van Benthem - 1983 - Distributed in the U.S.A. By Humanities Press.
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Finite Model Theory.Heinz-Dieter Ebbinghaus & Jörg Flum - 2001 - Studia Logica 69 (3):449-449.
Undecidability of Some Simple Formalized Theories.A. Janiczak - 1957 - Journal of Symbolic Logic 22 (2):217-217.

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