Join-completions of ordered algebras

2017/08/16 by José Gil-Férez, Gil-Férez, José, Luca Spada +5
Mathematics · #03B47 #03G10 #06F05 #06F15 #08B15 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03B47 #msc:03G10 #msc:06F05 #msc:06F15 #msc:08B15

paper · pdf · doi:10.48550/arxiv.1708.04990

arxiv created 2017/08/16 · arxiv updated 2017/08/17

Abstract

We present a systematic study of join-extensions and join-completions of ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind-MacNeille completion to the proof of the finite embeddability property for a number of varieties of ordered algebras.

Related

• Meet-completions and ordered domain algebras
• Model completions for universal classes of algebras: necessary and sufficient conditions
• Semilattice ordered algebras with constants
• Joinings classification and applications [after Einsiedler and Lindenstruass]
• Preservation of superamalgamation by expansions