Non-elementary classes of representable posets

Egrot, Rob

doi:10.1090/proc/13636

Non-elementary classes of representable posets
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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 $\beta$.

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