## Non-elementary classes of representable posets

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**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 $\beta$.

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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