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Tameness in generalized metric structures

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Abstract

We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways, chiefly by allowing the metric to take values in a well-behaved quantale. As a proof of concept we show that the result of Boney and Zambrano (Around the set-theoretical consistency of d-tameness of metric abstract elementary classes, arXiv:1508.05529, 2015) on (metric) tameness under a large cardinal assumption holds in this more general context. We briefly consider a further generalization to partial metric spaces, and hint at connections to classes of fuzzy structures, and structures on sheaves.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic

    Michael Lieberman

  2. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

    Jiří Rosický

  3. Departamento de Matemáticas, Universidad Nacional de Colombia, AK 30 # 45-03 código postal, 111321, Bogota, Colombia

    Pedro Zambrano

Authors
  1. Michael Lieberman
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  2. Jiří Rosický
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  3. Pedro Zambrano
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Correspondence to Michael Lieberman.

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M. Lieberman and J. Rosický were supported by the Grant Agency of the Czech Republic under the Grant P201/12/G028. P. Zambrano was supported by Universidad Nacional de Colombia under the Grants 41705 and 48359.

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Lieberman, M., Rosický, J. & Zambrano, P. Tameness in generalized metric structures. Arch. Math. Logic 62, 531–558 (2023). https://doi.org/10.1007/s00153-022-00852-4

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