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Order, 2008
A Heyting algebra \(A\) is called completely join-prime generated if every element of \(A\) is a join of completely join-prime elements of \(A\). Theorem 2.12 of this paper characterizes complete and completely join-prime generated Heyting algebras in two different ways.
Bezhanishvili, G., Bezhanishvili, N.
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A Heyting algebra \(A\) is called completely join-prime generated if every element of \(A\) is a join of completely join-prime elements of \(A\). Theorem 2.12 of this paper characterizes complete and completely join-prime generated Heyting algebras in two different ways.
Bezhanishvili, G., Bezhanishvili, N.
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Studia Logica, 2021
The author introduces a class of inquisitive Heyting algebras as algebraic structures of inquisitive superintuitionistic logics. These algebras are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. The author gives some equivalent characterizations of Heyting algebras.
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The author introduces a class of inquisitive Heyting algebras as algebraic structures of inquisitive superintuitionistic logics. These algebras are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. The author gives some equivalent characterizations of Heyting algebras.
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Functional monadic Heyting algebras
Algebra Universalis, 2002A Heyting algebra is a bounded distributive lattice with the operation of relative pseudocomplementation. A monadic Heyting algebra is a Heyting algebra equipped with two unary operations \(\Delta \) and \(\nabla \) satisfying the conditions (i) \(\Delta \nabla a = \nabla a\) (ii) \(\nabla \Delta a = \Delta a\) (iii) \(\nabla (\nabla a\wedge b ...
Bezhanishvili, Guram, Harding, John
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2023
Submission note: A thesis submitted in total fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Engineering and Mathematical Sciences, College of Science, Health and Engineering, La Trobe University, Bundoora, Victoria.This thesis was a recipient of the Nancy Millis Award for theses of exceptional merit.
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Submission note: A thesis submitted in total fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Engineering and Mathematical Sciences, College of Science, Health and Engineering, La Trobe University, Bundoora, Victoria.This thesis was a recipient of the Nancy Millis Award for theses of exceptional merit.
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Grothendieck-like duality for Heyting algebras
Algebra Universalis, 2002A. Brezuleanu and R. Diaconescu established a sheaf duality theory for the category of bounded distributive lattices. Their ideas come from the well-known Grothendieck duality of commutative rings. The multipliers in lattice theory were used by J. Schmid in order to give a construction of the maximal lattice of quotients for a distributive lattice.
DI NOLA, Antonio, G. GEORGESCU
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I n -symmetrical Heyting algebras
Algebra Universalis, 1992A symmetrical Heyting algebra is an algebra \((A;\land,\lor,',\Rightarrow,0,1)\) such that \((A;\land,\lor,\Rightarrow,0,1)\) is a Heyting algebra and \((A;\land,\lor,',0,1)\) is a DeMorgan algebra. The Heyting algebra is \(I_ n\)-symmetrical if it satisfies the Ivo Thomas equality. The authors show that these algebras are semi-simple.
Savini, Sonia +2 more
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Heyting Algebras with Operators
MLQ, 2001In this paper, the author studies Heyting algebras with unary operators, that is, algebras \({\mathbf A}= ({\mathbf {A'}},M)\), where \({\mathbf {A'}}\) is a Heyting algebra and \(M\) is a finite set of unary operators \(m_1,\dots, m_k\). A general description of subdirectly irreducible Heyting algebras with operators is given under some conditions ...
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On self‐distributive weak Heyting algebras
Mathematical Logic Quarterly, 2023AbstractWe use the left self‐distributive axiom to introduce and study a special class of weak Heyting algebras, called self‐distributive weak Heyting algebras (SDWH‐algebras). We present some useful properties of SDWH‐algebras and obtain some equivalent conditions of them. A characteristic of SDWH‐algebras of orders 3 and 4 is given. Finally, we study
Mohsen Nourany +2 more
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2017
In this paper, we introduce the concept of fuzzy Heyting algebra (FHA) as an extension of Heyting algebra. We also characterize fuzzy Heyting algebra using the properties of Heyting algebra(HA) and distributive fuzzy lattices. We, finally, state and prove some results on fuzzy Heyting algebra.
Berhanu Assaye Alaba +1 more
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In this paper, we introduce the concept of fuzzy Heyting algebra (FHA) as an extension of Heyting algebra. We also characterize fuzzy Heyting algebra using the properties of Heyting algebra(HA) and distributive fuzzy lattices. We, finally, state and prove some results on fuzzy Heyting algebra.
Berhanu Assaye Alaba +1 more
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Compact Hausdorff Heyting algebras
Algebra universalis, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bezhanishvili, Guram, Harding, John
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