Free p-algebras revisited: An algebraic investigation of implication-free intuitionism

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-05-08 DOI:10.1016/j.apal.2025.103610

Tomasz Kowalski , Katarzyna Słomczyńska

引用次数: 0

Abstract

We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra terms, simpler proofs of several existing results. As a by-product, we obtain an isomorphism between the free pseudocomplemented semilattice and the poset of join-irreducibles of the free p-algebra augmented by zero.

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重访自由p-代数：无蕴涵直觉主义的代数研究

给出了自由分配p-代数的一个新构造。我们的构造依赖于对完全满足不可约同余的详细描述，因此它是纯粹的普适代数。它给出了p代数项的一个标准形式定理，对几个已有结果的更简单的证明。作为副产物，我们得到了自由伪补半格与自由增0 p代数的联合不可约正集之间的同构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.