Geodesic
Compounding Objects
Bulletin of the Section of Logic, Tome 49 (2020) no. 2.

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We prove a characterization theorem for filters, proper filters and ultrafilters which is a kind of converse of Łoś's theorem. It is more natural than the usual intuition of these terms as large sets of coordinates, which is actually unconvincing in the case of ultrafilters. As a bonus, we get a very simple proof of Łoś's theorem.
Keywords: Łoś's theorem, converse of Łoś's theorem, filter, proper filter, ultrafilter 
@article{BSL_2020_49_2_a2,
     author = {\v{S}iki\'c, Zvonimir},
     title = {Compounding {Objects}},
     journal = {Bulletin of the Section of Logic},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2020_49_2_a2/}
}
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Šikić, Zvonimir. Compounding Objects. Bulletin of the Section of Logic, Tome 49 (2020) no. 2. http://geodesic.mathdoc.fr/item/BSL_2020_49_2_a2/