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A note on the non‐forking‐instances topology
Author(s) -
Shami Ziv
Publication year - 2020
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.202000011
Subject(s) - topology (electrical circuits) , general topology , mathematics , product topology , invariant (physics) , reduct , initial topology , open set , covering space , extension topology , simple (philosophy) , topological space , discrete mathematics , pure mathematics , computer science , combinatorics , data mining , rough set , philosophy , epistemology , mathematical physics
The non‐forking‐instances topology (NFI topology) 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 [6] to describe the set of universal transducers for ( T , T − ) (invariants sets that translate 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 weak non‐finite cover property (wnfcp), the topology is invariant over ⌀ in T − .