TY - JOUR

T1 - A note on the non-forking-instances topology

AU - Shami, Ziv

N1 - Publisher Copyright:
© 2020 Wiley-VCH GmbH

PY - 2020/10/1

Y1 - 2020/10/1

N2 - The non-forking-instances topology (NFI topology) is a topology on the Stone space of a theory T that depends on a reduct (Formula presented.) of T. This topology has been used in [6] to describe the set of universal transducers for (Formula presented.) (invariants sets that translate forking-open sets in (Formula presented.) 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 (Formula presented.) 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 (Formula presented.) in (Formula presented.).

AB - The non-forking-instances topology (NFI topology) is a topology on the Stone space of a theory T that depends on a reduct (Formula presented.) of T. This topology has been used in [6] to describe the set of universal transducers for (Formula presented.) (invariants sets that translate forking-open sets in (Formula presented.) 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 (Formula presented.) 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 (Formula presented.) in (Formula presented.).

UR - http://www.scopus.com/inward/record.url?scp=85091611339&partnerID=8YFLogxK

U2 - 10.1002/malq.202000011

DO - 10.1002/malq.202000011

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AN - SCOPUS:85091611339

SN - 0942-5616

VL - 66

SP - 336

EP - 340

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

IS - 3

ER -