Heyting Algebras : Duality Theory. 1st ed. 2019

種類:

電子ブック

責任表示:

by Leo Esakia ; edited by Guram Bezhanishvili, Wesley H. Holliday

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Esakia, Leo.
• Bezhanishvili, Guram.
• Holliday, Wesley H.
• SpringerLink (Online service)

シリーズ名:

Trends in Logic, Studia Logica Library ; 50

ISBN:

9783030120962 [3030120961]    

注記:

Foreword -- Editor's Note -- Introduction -- Chapter 1. Preliminary Notions and Necessary Facts -- Chapter 2. Heyting Algebras and Closure Algebras -- Chapter 3. Duality Theory: Hybrids -- Appendix -- Bibliography.
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 c

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