Ultrafilter extensions of linear orders

Denis I. Saveliev

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arXiv · 1310.4533

Ultrafilter extensions of linear orders

Denis I. Saveliev

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Abstract

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.

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BibTeX RIS

Denis I. Saveliev. 2013-10-16. Ultrafilter extensions of linear orders. https://arxiv.org/abs/1310.4533

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