Smooth measures and the canonical retraction in NIP theories

2024/01/13 by Xavier Pigé, Pigé, Xavier
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2401.07025

openalex publication_date 2024/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the results proved by Simon on the canonical retraction F_M from the space of M-invariant types onto the space of types finitely satisfiable in M remain true over measures. We also make another construction of the canonical retraction for measures, mimicking what Simon did for types, and show that it coincides with Simon's canonical retraction for measures. To do so, we make extensive use of smooth measures.

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