Abstract
It has been shown recently that monodic first-order temporal logic without functional symbols but with equality is incomplete, i.e., the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic two-variable formulae is not recursively enumerable.
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Degtyarev, A., Fisher, M. & Lisitsa, A. Equality and Monodic First-Order Temporal Logic. Studia Logica 72, 147–156 (2002). https://doi.org/10.1023/A:1021352309671
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DOI: https://doi.org/10.1023/A:1021352309671