Epimorphism Surjectivity in Varieties of Heyting Algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00532809" target="_blank" >RIV/67985807:_____/20:00532809 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.apal.2020.102824" target="_blank" >http://dx.doi.org/10.1016/j.apal.2020.102824</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apal.2020.102824" target="_blank" >10.1016/j.apal.2020.102824</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Epimorphism Surjectivity in Varieties of Heyting Algebras

Popis výsledku v původním jazyce

It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K. It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show that for every integer n⩾2, the variety of all Heyting algebras of width at most n has a non-surjective epimorphism. Within the so-called Kuznetsov-Gerčiu variety (i.e., the variety generated by finite linear sums of one-generated Heyting algebras), we describe exactly the subvarieties that have surjective epimorphisms. This yields new positive examples, and an alternative proof of epimorphism surjectivity for all varieties of Gödel algebras. The results settle natural questions about Beth-style definability for a range of intermediate logics.

Název v anglickém jazyce

Epimorphism Surjectivity in Varieties of Heyting Algebras

Popis výsledku anglicky

It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K. It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show that for every integer n⩾2, the variety of all Heyting algebras of width at most n has a non-surjective epimorphism. Within the so-called Kuznetsov-Gerčiu variety (i.e., the variety generated by finite linear sums of one-generated Heyting algebras), we describe exactly the subvarieties that have surjective epimorphisms. This yields new positive examples, and an alternative proof of epimorphism surjectivity for all varieties of Gödel algebras. The results settle natural questions about Beth-style definability for a range of intermediate logics.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF17_050%2F0008361" target="_blank" >EF17_050/0008361: Rozvoj lidských zdrojů pro výzkum v teoretické informatice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Annals of Pure and Applied Logic

ISSN

0168-0072

e-ISSN

—

Svazek periodika

171

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

31

Strana od-do

102824

Kód UT WoS článku

000553439500003

EID výsledku v databázi Scopus

2-s2.0-85084860827