Submission date: 15 February 2020

Abstract:

The NFI-topology, introduced in [S0], is a topology on the Stone space of a theory T that depends on a reduct T^- of T. This topology has been used in [S0] to describe the set of universal transducers for (T,T^-) (invariants sets that translates forking-open sets in T^- to forking-open sets in T). In this paper we show that in contrast to the stable case, the NFI-topology need not be invariant over parameters in T^- but a weak version of this holds for any simple T. We also note that for the lovely pair expansions, of theories with the wnfcp , the topology is invariant over ∅ in T^-.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 2002.06389: pdf, ps.