  Propositional temporal logic over the real number time flow is finitely
axiomatisable, but its first-order counterpart is not recursively
axiomatisable. We study the logic that combines the propositional
axiomatisation with the usual axioms for first-order logic with identity, and
develop an alternative ``admissible'' semantics for it, showing that it is
strongly complete for admissible models over the reals. By contrast there is no
recursive axiomatisation of the first-order temporal logic of admissible models
whose time flow is the integers, or any scattered linear ordering.
