无限双heyting代数

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2025-05-09 DOI:10.1007/s00012-025-00892-w

Lydia Tasiou

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引用次数: 0

摘要

如果包含x的最小逆集（即逆集和逆集）是有限的，那么我们说一个偏集\({\mathbb {X}}\)是之字形像有限的，对于所有\(x\in X.\)我们证明了一个双heyting代数是无限的当且仅当它与一个之字形像有限偏集的逆集的格同构。之字形像有限序集具有有限连通序集的不相交并的性质。因此，我们等价地证明了一个双heyting代数是无限的当且仅当它同构于简单有限双heyting代数的直积。

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Profinite bi-Heyting algebras

A poset \({\mathbb {X}}\) is said to be zigzag image-finite, if the least updownset (i.e., both an upset and a downset) containing x is finite, for all \(x\in X.\) We show that a bi-Heyting algebra is profinite if and only if it is isomorphic to the lattice of upsets of a zigzag image-finite poset. Zigzag image-finite posets have the property of being disjoint unions of finite connected posets. Because of this, we equivalently show that a bi-Heyting algebra is profinite if and only if it is isomorphic to a direct product of simple finite bi-Heyting algebras.

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来源期刊

Algebra Universalis 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3 months

期刊介绍： Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.