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Preprint Number 2338
2338. Krzysztof Krupiński and Adrián Portillo Maximal stable quotients of invariant types in NIP theories E-mail: Submission date: 5 February 2023 Abstract: For a NIP theory T, a sufficiently saturated model ℂ of T, and an invariant (over some small subset of ℂ) global type p, we prove that there exists a finest relatively type-definable over a small set of parameters from ℂ equivalence relation on the set of realizations of p which has stable quotient. This is a counterpart for equivalence relations of the main result of the paper On maximal stable quotients of definable groups in NIP theories by M. Haskel and A. Pillay which shows the existence of maximal stable quotients of type-definable groups in NIP theories. Our proof adapts the ideas of the proof of this result, working with relatively type-definable subsets of the group of automorphisms of the monster model as defined in the paper On first order amenability by E. Hrushovski, K. Krupinski, and A. Pillay. Mathematics Subject Classification: Keywords and phrases: |
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