2013/10/16 by Denis I. Saveliev, Saveliev, Denis I.
Computer Science · Mathematics · #06B75 #54D80 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Primary: 06A05. Secondary: 03C55 #Rings, Modules, and Algebras #math.LO #msc:03C55 #msc:06A05. #msc:06B75 #msc:54D80 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1310.4533
arxiv created 2013/10/16 · openalex publication_date 2013/10/16 · arxiv updated 2013/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a technique allowing to obtain significant results in algebra and dynamics. Here we consider another particular case where the models are linearly ordered sets. We explicitly calculate the extensions of a given linear order and the corresponding operations of minimum and maximum on a set. We show that the extended relation is not more an order however is close to the natural linear ordering of nonempty half-cuts of the set and that the two extended operations define a skew lattice structure on the set of ultrafilters.