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A set-theoretic approach to algebraic L-domains

Published online by Cambridge University Press:  11 April 2024

Juan Zou ,
Yuhan Zhao ,
Cuixia Miao  and
Longchun Wang Open the ORCID record for Longchun Wang [Opens in a new window]
Juan Zou
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu, China
Yuhan Zhao
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu, China
Cuixia Miao
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu, China
Longchun Wang*
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu, China
*
Corresponding author: Longchun Wang; Email: longchunw@163.com
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Abstract

In this paper, the notion of locally algebraic intersection structure is introduced for algebraic L-domains. Essentially, every locally algebraic intersection structure is a family of sets, which forms an algebraic L-domain ordered by inclusion. It is shown that there is a locally algebraic intersection structure which is order-isomorphic to a given algebraic L-domain. This result extends the classic Stone’s representation theorem for Boolean algebras to the case of algebraic L-domains. In addition, it can be seen that many well-known representations of algebraic L-domains, such as logical algebras, information systems, closure spaces, and formal concept analysis, can be analyzed in the framework of locally algebraic intersection structures. Then, a set-theoretic uniformity across different representations of algebraic L-domains is established.

Keywords

Stone’s representation theoremdomain theoryalgebraic L-domainalgebraic intersection structure

Information

Type
Special Issue: TAMC 2022
Information
Mathematical Structures in Computer Science , Volume 34 , Special Issue 3: Theory and Applications of Models of Computation , March 2024 , pp. 244 - 257
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Footnotes

*

Supported by Shandong Provincial Natural Science Foundation (ZR2023MA051, ZR2022MA022).

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