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Heyting Algebras

Duality Theory. Trends in Logic 50

By (author) Leo Esakia
Translated by Anton Evseev
Format: Hardback
Language: English
Publisher: Springer Nature Switzerland AG, Cham, Switzerland
Published: 17th Jul 2019
Dimensions: w 156mm h 234mm d 8mm
Weight: 338g
ISBN-10: 3030120953
ISBN-13: 9783030120955
Barcode No: 9783030120955
Synopsis
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 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.

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