 Few axiomatizable, and even fewer decidable, natural fragments of first-order temporal logics have been identified and investigated so far. These include first-order temporal logics with Since and Until over the class of all linear flows of time and over the order of the rationals (Merz 1992; Reynolds 1996), the fragment T(FOs) of FOTL, where temporal operators may not occur inside the scope of a quantifier (Gabbay et al. 1994, Chapter 14), as well as the monodic fragment, only allowing formulae with at most one free variable in the scope of a temporal operator (see Hodkinson et al. 2000; 2001; 2002 and Wolter and Zakharyaschev 2002). Still, as shown in the latter paper, already the monodic fragment with equality is no longer recursively axiomatizable. For further decidability results for suitably restricted fragments of FOTL, see Hodkinson et al. (2000). Additional technical references are given in Gabbay et al. (1994, Chapter 14) and Kröger and Merz (2008). For completeness results for first-order modal logics see also Fitting and Mendelsohn (1998) and the entry on  modal logic.