Ordered spaces and frames
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Sources and background

Esakia duality and free Heyting algebras

Esakia duality presents a spatial and combinatorial way of representing Heyting algebras, using special compact ordered spaces. Other dualities exist, which employ other representations, such as Bellissima’s, and Ghilardi’s finitely presented duality.

References

  1. Leo Esakia (2019)
    Heyting Algebras: Duality Theory.
    Trends in Logic, vol. 50. Edited by Guram Bezhanishvili and Wesley H. Holliday; translated by Anton Evseev. Springer, Cham.
    DOI
  2. Nick Bezhanishvili (2006)
    Lattices of Intermediate and Cylindric Modal Logics.
    PhD thesis, Universiteit van Amsterdam. ILLC Dissertation Series DS-2006-02. ISBN 978-90-5776-147-8.
    Thesis
  3. Fabio Bellissima (1986)
    Finitely generated free Heyting algebras.
    The Journal of Symbolic Logic 51(1), 152–165.
    DOI
  4. Luck Darnière and Markus Junker (2010)
    On Bellissima’s construction of the finitely generated free Heyting algebras, and beyond.
    Archive for Mathematical Logic 49(7–8), 743–771.
    DOI
  5. R. Elageili and J. K. Truss (2012)
    Finitely generated free Heyting algebras: the well-founded initial segment.
    The Journal of Symbolic Logic 77(4), 1291–1307.
    DOI
  6. Silvio Ghilardi and Luigi Santocanale (2020)
    Free Heyting algebra endomorphisms: Ruitenburg’s Theorem and beyond.
    Mathematical Structures in Computer Science 30(6), 572–596.
    DOI
  7. Guram Bezhanishvili and Revaz Grigolia (2005)
    Locally finite varieties of Heyting algebras.
    Algebra Universalis 54(4), 465–473. Problem 2.4 asks whether every 2-finite variety of Heyting algebras is locally finite.
    DOI
  8. Tapani Hyttinen, Miguel Martins, Tommaso Moraschini, and Davide E. Quadrellaro (2026)
    Strictly n-finite varieties of Heyting algebras.
    The Journal of Symbolic Logic 91(1), 473–488. First published online 29 October 2024; §4 describes the related layered Esakia spaces.
    DOI