Heyting代数的布尔原子及其应用

doi:10.6040/j.issn.1671-9352.0.2020.031

摘要/Abstract

摘要： 利用Heyting代数的布尔元得到了Heyting代数的一种直积分解表示。基于Heyting代数的这种分解,证明了有限Heyting代数可通过依次替换布尔代数中的原子为Heyting代数而得到。该结论揭示了Heyting代数与布尔代数之间的一种新的关系。

关键词: Heyting代数, 布尔代数, 布尔原子, 替换

Abstract: A kind of direct product decomposition of Heyting algebras is obtained using the Boolean elements of Heyting algebras. Based on this decomposition of Heyting algebras, it is proved that a finite Heyting algebra can be obtained by substituting the atoms of a Boolean algebra with Heyting algebras. This conclusion reveals a kind of new relationship between Heyting algebras and Boolean algebras.

Key words: Heyting algebra, Boolean algebra, Boolean atom, substitution

中图分类号:

O153.2

赵马盼,樊丰丽,颉永建. Heyting代数的布尔原子及其应用[J]. 《山东大学学报(理学版)》, 2020, 55(5): 71-80.

ZHAO Ma-pan, FAN Feng-li, XIE Yong-jian. Boolean atoms of Heyting algebras and their application[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 71-80.

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