Overview
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 logic. 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 firstof 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.
Full Product Details
Author: Leo Esakia ,
Guram Bezhanishvili ,
Wesley H. Holliday ,
Anton Evseev
Publisher: Springer Nature Switzerland AG
Imprint: Springer Nature Switzerland AG
Edition: 1st ed. 2019
Volume: 50
Weight: 0.454kg
ISBN: 9783030120955
ISBN 10: 3030120953
Pages: 95
Publication Date: 17 July 2019
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Language: English
Reviews
Presenting in a succinct style the brilliant ideas of the author, this book provides an indispensable authentic source for researchers working on dualities between ordered and topological structures with impact on mathematical logic. (Marcel Erne, Mathematical Reviews, June, 2021)
Leo Esakia's classic monograph is extremely welcome and I hope that it will be widely read. ... Moreover, the exposition, in Esakia's own words and in its entirety, has insights to offer to experienced researchers and relative novices alike. ... Esakia's Introduction to Heyting Algebras. Duality Theory makes interesting reading for its scope and its vision. ... The translation brings subsidiary benefits. (Hilary A. Priestley, Studia Logica, Vol. 109, 2021) Presenting in a succinct style the brilliant ideas of the author, this book provides an indispensable authentic source for researchers working on dualities between ordered and topological structures with impact on mathematical logic. (Marcel Erne, Mathematical Reviews, June, 2021)
