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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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