On the forking topology of a reduct of a simple theory

Ziv Shami

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Let T be a simple L-theory and let T- be a reduct of T to a sublanguage L- of L. For variables x, we call an ∅ -invariant set Γ (x) in C a universal transducer if for every formula ϕ-(x, y) ∈ L- and every a, ϕ-(x,a)L--forksover∅iffΓ(x)∧ϕ-(x,a)L-forksover∅.We show that there is a greatest universal transducer Γ ~ x (for any x) and it is type-definable. In particular, the forking topology on Sy(T) refines the forking topology on Sy(T-) for all y. Moreover, we describe the set of universal transducers in terms of certain topology on the Stone space and show that Γ ~ x is the unique universal transducer that is L--type-definable with parameters. If T- is a theory with the wnfcp (the weak nfcp) and T is the theory of its lovely pairs of models we show that Γ ~ x= (x= x) and give a more precise description of the set of universal transducers for the special case where T- has the nfcp.

Original languageEnglish
Pages (from-to)313-324
Number of pages12
JournalArchive for Mathematical Logic
Issue number3-4
StatePublished - 1 May 2020


  • Forking topology
  • Reduct
  • Universal transducer


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