國立高雄大學圖資館 |

Language: English

Back

Heyting algebrasduality theory /

Bezhanishvili, Guram.

Heyting algebrasduality theory /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Heyting algebrasby Leo Esakia ; edited by Guram Bezhanishvili, Wesley H. Holliday.
Reminder of title:	duality theory /
Author:	Esakia, Leo.
other author:	Bezhanishvili, Guram.
Published:	Cham :Springer International Publishing :2019.
Description:	xv, 95 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Heyting algebras.
Online resource:	https://doi.org/10.1007/978-3-030-12096-2
ISBN:	9783030120962$q(electronic bk.)

Heyting algebrasduality theory /
Esakia, Leo.

Heyting algebrasduality theory /[electronic resource] :by Leo Esakia ; edited by Guram Bezhanishvili, Wesley H. Holliday. - Cham :Springer International Publishing :2019. - xv, 95 p. :ill., digital ;24 cm. - Trends in logic, studia logica library,v.501572-6126 ;. - Trends in logic, studia logica library ;v.41..

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 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.

ISBN: 9783030120962$q(electronic bk.)

Standard No.: 10.1007/978-3-030-12096-2doiSubjects--Topical Terms:

849683
Heyting algebras.

LC Class. No.: QA162

Dewey Class. No.: 511.324

Heyting algebrasduality theory /
LDR:02538nmm a2200349 a 4500 001 563918
003 DE-He213
005 20191205171430.0
006 m d
007 cr nn 008maaau
008 200311s2019 gw s 0 eng d
020 $a 9783030120962$q(electronic bk.)
020 $a 9783030120955$q(hardback)
020 $a 9783030120986$q(paperback)
024 7 $a 10.1007/978-3-030-12096-2 $2 doi
035 $a 978-3-030-12096-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA162
072 7 $a HPL $2 bicssc
072 7 $a PHI011000 $2 bisacsh
072 7 $a QDTL $2 thema
082 0 4 $a 511.324 $2 23
090 $a QA162 $b .E74 2019
100 1 $a Esakia, Leo. $3 849682
245 1 0 $a Heyting algebras $h [electronic resource] : $b duality theory / $c by Leo Esakia ; edited by Guram Bezhanishvili, Wesley H. Holliday.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xv, 95 p. : $b ill., digital ; $c 24 cm.
490 1 $a Trends in logic, studia logica library, $x 1572-6126 ; $v v.50
505 0 $a 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.
520 $a 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.
650 0 $a Heyting algebras. $3 849683
650 1 4 $a Logic. $3 180785
650 2 4 $a Mathematical Logic and Foundations. $3 274479
650 2 4 $a Mathematical Logic and Formal Languages. $3 275383
700 1 $a Bezhanishvili, Guram. $3 683221
700 1 $a Holliday, Wesley H. $3 731400
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Trends in logic, studia logica library ; $v v.41. $3 680671
856 4 0 $u https://doi.org/10.1007/978-3-030-12096-2
950 $a Mathematics and Statistics (Springer-11649)