Esakia Duals of Regular Heyting Algebras

Gianluca Grilletti; Davide Emilio Quadrellaro

Esakia Duals of Regular Heyting Algebras

Gianluca Grilletti, Davide Emilio Quadrellaro

Tutkimustuotos: Työpaperi › Esipainos

Abstrakti

We investigate in this article regular Heyting algebras by means of Esakia duality. In particular, we provide some characterisations of Esakia spaces which are dual to regular Heyting algebras and we show that there are continuum-many varieties of Heyting algebras generated by regular Heyting algebras. We also study several logical applications of these classes of objects and we use them to provide novel topological completeness theorems for inquisitive logic, $\mathtt{DNA}$-logics and dependence logic.

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Tila	Julkaistu - 20 maalisk. 2023
OKM-julkaisutyyppi	Ei sovellu

Pääsy asiakirjaan

2303.11246v1

Siteeraa tätä

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title = "Esakia Duals of Regular Heyting Algebras",

abstract = " We investigate in this article regular Heyting algebras by means of Esakia duality. In particular, we provide some characterisations of Esakia spaces which are dual to regular Heyting algebras and we show that there are continuum-many varieties of Heyting algebras generated by regular Heyting algebras. We also study several logical applications of these classes of objects and we use them to provide novel topological completeness theorems for inquisitive logic, $\mathtt{DNA}$-logics and dependence logic. ",

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T1 - Esakia Duals of Regular Heyting Algebras

AU - Grilletti, Gianluca

AU - Quadrellaro, Davide Emilio

PY - 2023/3/20

Y1 - 2023/3/20

N2 - We investigate in this article regular Heyting algebras by means of Esakia duality. In particular, we provide some characterisations of Esakia spaces which are dual to regular Heyting algebras and we show that there are continuum-many varieties of Heyting algebras generated by regular Heyting algebras. We also study several logical applications of these classes of objects and we use them to provide novel topological completeness theorems for inquisitive logic, $\mathtt{DNA}$-logics and dependence logic.

AB - We investigate in this article regular Heyting algebras by means of Esakia duality. In particular, we provide some characterisations of Esakia spaces which are dual to regular Heyting algebras and we show that there are continuum-many varieties of Heyting algebras generated by regular Heyting algebras. We also study several logical applications of these classes of objects and we use them to provide novel topological completeness theorems for inquisitive logic, $\mathtt{DNA}$-logics and dependence logic.

KW - math.LO

KW - 06D20, 03C05, 03B55

M3 - Förtryck

BT - Esakia Duals of Regular Heyting Algebras

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