Heyting Algebras

Duality Theory

  • Leo Esakia
  • Guram Bezhanishvili
  • Wesley H. Holliday

Part of the Trends in Logic book series (TREN, volume 50)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Leo Esakia
    Pages 15-40
  3. Leo Esakia
    Pages 41-75
  4. Back Matter
    Pages 77-95

About this book


This book presents an English translation of a classic Russian text on duality theory

for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved

popular among Russian-speaking logicians. This translation helps make the ideas

accessible to a wider audience and pays tribute to an influential mind in mathematical


The book discusses the theory of Heyting algebras and closure algebras, as

well as the corresponding intuitionistic and modal logics. The author introduces the

key notion of a hybrid that “crossbreeds” topology (Stone spaces) and order (Kripke

frames), resulting in the structures now known as Esakia spaces. The main theorems

include a duality between the categories of closure algebras and of hybrids, and a duality

between the categories of Heyting algebras and of so-called strict hybrids.

Esakia’s book was originally published in 1985. It was the first of a planned two-volume monograph

on Heyting algebras. But after the collapse of the Soviet Union, the publishing house

closed and the project died with it. Fortunately, this important work now lives on in

this accessible translation. The Appendix of the book discusses the planned contents

of the lost second volume.


Heyting Algebra Intuitionistic Logic Intermediate Logics Modal Logic Closure Algebra Stone Space Esakia Space Esakia Duality Skeletal Closure Algebras Stone Space and Kripke Frame

Authors and affiliations

  • Leo Esakia
    • 1
  1. 1.(deceased)TbilisiGeorgia

Editors and affiliations

  • Guram Bezhanishvili
    • 1
  • Wesley H. Holliday
    • 2
  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA
  2. 2.Department of Philosophy and Group in Logic and the Methodology of ScienceUniversity of CaliforniaBerkeleyUSA

Bibliographic information