RT Journal Article
T1 Open core and small groups in dense pairs of topological structures
A1 Baro González, Elías
A1 Martin Pizarro, Amador
AB Dense pairs of geometric topological fields have tame open core, that is, every definable open subset in the pair is already definable in the reduct. We fix a minor gap in the published version of van den Dries's seminal work on dense pairs of o-minimal groups, and show that every definable unary function in a dense pair of geometric topological fields agrees with a definable function in the reduct, off a small definable subset, that is, a definable set internal to the predicate.For certain dense pairs of geometric topological fields without the independence property, whenever the underlying set of a definable group is contained in the dense-codense predicate, the group law is locally definable in the reduct as a geometric topological field. If the reduct has elimination of imaginaries, we extend this result, up to interdefinability, to all groups internal to the predicate
YR 2022
FD 2022-06-01
LK https://hdl.handle.net/20.500.14352/108621
UL https://hdl.handle.net/20.500.14352/108621
LA eng
NO Baro E, Martin-Pizarro A. Open core and small groups in dense pairs of topological structures. Annals of Pure and Applied Logic 2021;172:102858. https://doi.org/10.1016/j.apal.2020.102858.
DS Docta Complutense
RD 26 abr 2025