Profiniteness and representability of spectra of Heyting algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00545611" target="_blank" >RIV/67985807:_____/21:00545611 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.aim.2021.107959" target="_blank" >http://dx.doi.org/10.1016/j.aim.2021.107959</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aim.2021.107959" target="_blank" >10.1016/j.aim.2021.107959</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Profiniteness and representability of spectra of Heyting algebras

Popis výsledku v původním jazyce

We prove that there exist profinite Heyting algebras that are not isomorphic to the profinite completion of any Heyting algebra. This resolves an open problem from 2009. More generally, we characterize those varieties of Heyting algebras in which profinite algebras are isomorphic to profinite completions. It turns out that there exists largest such. We give different characterizations of this variety and show that it is finitely axiomatizable and locally finite. From this it follows that it is decidable whether in a finitely axiomatizable variety of Heyting algebras all profinite members are profinite completions. In addition, we introduce and characterize representable varieties of Heyting algebras, thus drawing connection to the classical problem of representing posets as prime spectra.

Název v anglickém jazyce

Profiniteness and representability of spectra of Heyting algebras

Popis výsledku anglicky

We prove that there exist profinite Heyting algebras that are not isomorphic to the profinite completion of any Heyting algebra. This resolves an open problem from 2009. More generally, we characterize those varieties of Heyting algebras in which profinite algebras are isomorphic to profinite completions. It turns out that there exists largest such. We give different characterizations of this variety and show that it is finitely axiomatizable and locally finite. From this it follows that it is decidable whether in a finitely axiomatizable variety of Heyting algebras all profinite members are profinite completions. In addition, we introduce and characterize representable varieties of Heyting algebras, thus drawing connection to the classical problem of representing posets as prime spectra.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Advances in Mathematics

ISSN

0001-8708

e-ISSN

1090-2082

Svazek periodika

391

Číslo periodika v rámci svazku

19 November 2021

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

47

Strana od-do

107959

Kód UT WoS článku

000701013100008

EID výsledku v databázi Scopus

2-s2.0-85113372379