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  1. Inexpressiveness of First-Order Fragments.William C. Purdy - 2006 - Australasian Journal of Logic 4 (5):1-12.
    It is well-known that first-order logic is semi-decidable. Therefore, first-order logic is less than ideal for computational purposes. Certain fragments of first-order logic are of interest because they are decidable. But decidability is gained at the cost of expressiveness. The objective of this paper is to investigate inexpressiveness of fragments that have received much attention.
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  • Axiomatizing the Monodic Fragment of First-Order Temporal Logic.Frank Wolter & Michael Zakharyaschev - 2002 - Annals of Pure and Applied Logic 118 (1-2):133-145.
    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 fragment is an exception by constructing its finite Hilbert-style axiomatization. We also show that the monodic fragment with equality is not recursively axiomatizable.
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