Densification via polynomials, languages, and frames

Autor:	Nikolaos Galatos, Rostislav Horčík
Rok vydání:	2022
Předmět:	Pure mathematics Algebra and Number Theory Corollary Completeness (order theory) Countable set Algebraic number Total order Commutative property Mathematics
Zdroj:	Journal of Pure and Applied Algebra. 226:106852
ISSN:	0022-4049
DOI:	10.1016/j.jpaa.2021.106852
Popis:	It is known that every countable totally ordered set can be embedded into a countable dense one. We extend this result to totally ordered commutative monoids and to totally ordered commutative residuated lattices (the latter result fails in the absence of commutativity). The latter has applications to density elimination of semilinear substructural logics. In particular we obtain as a corollary a purely algebraic proof of the standard completeness of uninorm logic; the advantage over the known proof-theoretic proof and the semantical proof is that it is extremely short and transparent and all details can be verified easily using standard algebraic constructions .
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::207cda185f88517546500416d5abf765 https://doi.org/10.1016/j.jpaa.2021.106852 Zobrazit plný text záznamu Full Text from ScienceDirect