δ-uniform BSS machines

A δ-uniform BSS machine is a standard BSS machine which does not rely on exact equality tests. We prove that, for any real closed archimedean field R, a set is δ-uniformly semi-decidable iff it is open and semi-decidable by a BSS machine which is locally time bounded; we also prove that the local time bound is nontrivial. This entails a number of results about BSS machines, in particular the existence of decidable sets whose interior (closure) is not even semi-decidable without adding constants. Finally, we show that the sets semi-decidable by Turing machines are the sets semi-decidable by δ-uniform machines with coefficients in Q or T, the field of Turing computable numbers.