Počet záznamů: 1
Profiniteness and representability of spectra of Heyting algebras
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SYSNO ASEP 0545611 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Profiniteness and representability of spectra of Heyting algebras Tvůrce(i) Bezhanishvili, G. (US)
Bezhanishvili, N. (NL)
Moraschini, T. (ES)
Stronkowski, Michał (UIVT-O)Číslo článku 107959 Zdroj.dok. Advances in Mathematics. - : Elsevier - ISSN 0001-8708
Roč. 391, 19 November 2021 (2021)Poč.str. 47 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova Heyting algebra ; Profinite algebra ; Profinite completion ; Representation Problem ; Priestley space ; Esakia space Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics Způsob publikování Open access Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000701013100008 EID SCOPUS 85113372379 DOI 10.1016/j.aim.2021.107959 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2022 Elektronická adresa http://dx.doi.org/10.1016/j.aim.2021.107959
Počet záznamů: 1