Densification via polynomials, languages, and frames

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00350847" target="_blank" >RIV/68407700:21230/22:00350847 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jpaa.2021.106852" target="_blank" >https://doi.org/10.1016/j.jpaa.2021.106852</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2021.106852" target="_blank" >10.1016/j.jpaa.2021.106852</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Densification via polynomials, languages, and frames

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Densification via polynomials, languages, and frames

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Výzkumné centrum informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

1873-1376

Svazek periodika

226

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

26

Strana od-do

—

Kód UT WoS článku

000704010100006

EID výsledku v databázi Scopus

2-s2.0-85111270087