East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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NOTE ON THE UNIQUENESS OF A UNIVERSAL SEP-COVER

  • Junguk Lee (Department of Mathematics, Changwon National University)
  • Received : 2023.07.21
  • Accepted : 2023.09.20
  • Published : 2023.09.30
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Abstract

In the case that the set of sorts is countable, we will prove that any sorted profinite group has the unique SEP-cover using the notion of prime model in model theory.

Keywords

Acknowledgement

This research was supported by Changwon National University in 2023-2024. The author thanks the referees for their careful reading and all the comments and suggestions.

References

  1. Z. Chatzidakis, Model theory of profinite groups having the Iwasawa property, Illinois J. Math., 42 (1998), 70-96.
  2. J. Dobrowolski, D. M. Hoffmann, J. Lee, Elementary equivalence theorem for PAC structures, J. Symb. Log., 85 (2020), 1467-1498. https://doi.org/10.1017/jsl.2020.61
  3. D. Haran and A. Lubotzky, Embedding covers and the theory of Frobenius fields, Israel J. Math., 41 (1982), 181-202. https://doi.org/10.1007/BF02771720
  4. D. M. Hoffmann and J. Lee, Co-theory of sorted profinite groups for PAC structures, J. Math. Log., 23 (2023), Paper No. 2250030, 60 pp.
  5. J. Lee, The embedding property for sorted profinite groups, J. Symb. Log., 88 (2023), 1005-1037. https://doi.org/10.1017/jsl.2023.16