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Non-elementary classes of representable posets


Author: Rob Egrot
Journal: Proc. Amer. Math. Soc. 145 (2017), 4675-4685
MSC (2010): Primary 06A11, 03G10; Secondary 03C20
DOI: https://doi.org/10.1090/proc/13636
Published electronically: May 30, 2017
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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
Email: robert.egr@mahidol.ac.th

DOI: https://doi.org/10.1090/proc/13636
Keywords: Poset, representation, axiomatization, ultrapower
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
Article copyright: © Copyright 2017 American Mathematical Society