Abstract
It is known that nontrivial ultraproducts of complete partially ordered sets (posets) are almost never complete. We show that complete additivity of functions is preserved in ultraproducts of posets. Since failure of this property is clearly preserved by ultraproducts, this implies that complete additivity of functions is an elementary property.
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Presented by P. P. Pálfy.
We dedicate this paper to Ervin Fried, teacher and friend
We thank the referee for useful suggestions and for a question that led to Corollary 3.
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Andréka, H., Gyenis, Z. & Németi, I. Ultraproducts of continuous posets. Algebra Univers. 76, 231–235 (2016). https://doi.org/10.1007/s00012-016-0401-4
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DOI: https://doi.org/10.1007/s00012-016-0401-4