Epimorphism Surjectivity in Varieties of Heyting Algebras
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Epimorphism Surjectivity in Varieties of Heyting Algebras
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/EF17_050%2F0008361" target="_blank" >EF17_050/0008361: Enhancing human resources for research in theoretical computer science</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Pure and Applied Logic
ISSN
0168-0072
e-ISSN
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Volume of the periodical
171
Issue of the periodical within the volume
9
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
31
Pages from-to
102824
UT code for WoS article
000553439500003
EID of the result in the Scopus database
2-s2.0-85084860827