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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The $\omega$-Vaught’s conjecture
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by David Gonzalez and Antonio Montalbán
Trans. Amer. Math. Soc. 376 (2023), 5989-6008
DOI: https://doi.org/10.1090/tran/8950
Published electronically: May 31, 2023

Abstract:

We introduce the $\omega$-Vaught’s conjecture, a strengthening of the infinitary Vaught’s conjecture. We believe that if one were to prove the infinitary Vaught’s conjecture in a structural way without using techniques from higher recursion theory, then the proof would probably be a proof of the $\omega$-Vaught’s conjecture. We show the existence of an equivalent condition to the $\omega$-Vaught’s conjecture and use this tool to show that all infinitary sentences whose models are linear orders satisfy the $\omega$-Vaught’s conjecture.
References
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Bibliographic Information
  • David Gonzalez
  • Affiliation: University of California, Berkeley, 110 Sproul Hall #5800, Berkeley, California 94720-5800
  • MR Author ID: 1326514
  • Email: david_gonzalez@berkeley.edu
  • Antonio Montalbán
  • Affiliation: University of California, Berkeley, Berkeley, California 94720-5800
  • ORCID: 0000-0002-5068-1444
  • Email: antonio@math.berkeley.edu
  • Received by editor(s): November 3, 2022
  • Received by editor(s) in revised form: March 7, 2023
  • Published electronically: May 31, 2023
  • Additional Notes: The second author was partially supported by NSF grant DMS-1363310.
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 5989-6008
  • MSC (2020): Primary 03D45, 03C75
  • DOI: https://doi.org/10.1090/tran/8950
  • MathSciNet review: 4630765