关于自分配弱Heyting代数

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2023-08-02 DOI:10.1002/malq.202200073

Mohsen Nourany, Shokoofeh Ghorbani, Arsham Borumand Saeid

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引用次数: 0

摘要

利用左自分配公理引入并研究了一类特殊的弱Heyting代数，称为自分配弱Heytin代数（SDWH代数）。我们给出了SDWH代数的一些有用性质，并得到了它们的一些等价条件。给出了3阶和4阶SDWH代数的一个特征。最后，我们研究了SDWH代数的多样性与一些已知的弱Heyting代数的子变种之间的关系，如Heyting代的多样性、基本代数的多样、子直格的多样性，自反WH代数（RWH代数）的多样性和传递WH代数（TWH代数）。

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On self-distributive weak Heyting algebras

We 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 the relation between the variety of SDWH-algebras and some of the known subvarieties of weak Heyting algebras such as the variety of Heyting algebras, the variety of basic algebras, the variety of subresiduated lattices, the variety of reflexive WH-algebras (RWH-algebras), and the variety of transitive WH-algebras (TWH-algebras).

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.