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Transactions of the American Mathematical Society Series B

Published by the American Mathematical Society since 2014, this gold open access electronic-only journal is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 2330-0000

The 2024 MCQ for Transactions of the American Mathematical Society Series B is 1.73.

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Characterizations of monadic NIP
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by Samuel Braunfeld and Michael C. Laskowski;
Trans. Amer. Math. Soc. Ser. B 8 (2021), 948-970
DOI: https://doi.org/10.1090/btran/94
Published electronically: November 2, 2021

Abstract:

We give several characterizations of when a complete first-order theory $T$ is monadically NIP, i.e. when expansions of $T$ by arbitrary unary predicates do not have the independence property. The central characterization is a condition on finite satisfiability of types. Other characterizations include decompositions of models, the behavior of indiscernibles, and a forbidden configuration. As an application, we prove non-structure results for hereditary classes of finite substructures of non-monadically NIP models that eliminate quantifiers.
References
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Bibliographic Information
  • Samuel Braunfeld
  • MR Author ID: 1197349
  • Michael C. Laskowski
  • MR Author ID: 110500
  • Received by editor(s): May 3, 2021
  • Received by editor(s) in revised form: August 5, 2021
  • Published electronically: November 2, 2021
  • Additional Notes: The second author was partially supported by NSF grant DMS-1855789
  • © Copyright 2021 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
  • Journal: Trans. Amer. Math. Soc. Ser. B 8 (2021), 948-970
  • MSC (2020): Primary 03C45
  • DOI: https://doi.org/10.1090/btran/94
  • MathSciNet review: 4334194