Ultraproducts of continuous posets
arXiv:1503.05578 · doi:10.1007/s00012-016-0401-4
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.