Axiomatizing the monodic fragment of first-order temporal logic Original Research Article

It is known that even seemingly small fragments of the first-order temporal logic over the natural numbers are not recursively enumerable. In this paper we show that the monodic (not monadic, where this result does not hold) fragment is an exception by constructing its finite Hilbert-style axiomatization. We also show that the monodic fragment with equality is not recursively axiomatizable.