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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Non-elementary classes of representable posets
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by Rob Egrot PDF
Proc. Amer. Math. Soc. 145 (2017), 4675-4685 Request permission

Abstract:

A poset is $(\omega ,C)$-representable if it can be embedded into a field of sets in such a way that all existing joins and all existing finite meets are preserved. We show that the class of $(\omega ,C)$-representable posets cannot be axiomatized in first order logic using the standard language of posets. We generalize this result to $(\alpha ,\beta )$-representable posets for certain values of $\alpha$ and $\beta$.
References
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Additional Information
  • Rob Egrot
  • Affiliation: Faculty of ICT, Mahidol University, 999 Phuttamonthon 4 Road, Salaya, Nakhon Pathom 73170, Thailand
  • MR Author ID: 975488
  • ORCID: 0000-0003-1170-8998
  • Email: robert.egr@mahidol.ac.th
  • Received by editor(s): July 18, 2016
  • Received by editor(s) in revised form: December 6, 2016
  • Published electronically: May 30, 2017
  • Communicated by: Mirna Džamonja
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 4675-4685
  • MSC (2010): Primary 06A11, 03G10; Secondary 03C20
  • DOI: https://doi.org/10.1090/proc/13636
  • MathSciNet review: 3691986