Heyting代数的Hyper-MacNeille补
Hyper-MacNeille Completions of Heyting algebras
摘要：
一个Heyting代数是可补的，如果每个元素$a$都有一个对偶伪补$a^+$;一个Heyting代数是中心可补的，如果它是可补的，并且每个可补都是中心可补的.我们表明，每个Heyting代数有一个中心补充的扩展在同一品种的Heyting代数作为原来的。我们使用这个工具来调查一种新的类型的完成的海廷代数的代数证明论的背景下产生的，所谓的超MacNeille完成。证明了Heyting代数的超MacNeille完备化是其中心补扩张的MacNeille完备化。这提供了一个代数描述的超麦克尼尔完成的海廷代数，允许发展的进一步性质的超麦克尼尔完成，并提供了新的例子品种的海廷代数是封闭的超麦克尼尔完成。特别是，中心补充的扩展和布尔积之间的连接，使我们能够证明，任何一种生成的Heyting代数是封闭的hyper-MacNeille完成。
英文摘要：
A Heyting algebra is supplemented if each element $a$ has a dual pseudo-complement $a^+$, and a Heyting algebra is centrally supplement if it is supplemented and each supplement is central. We show that each Heyting algebra has a centrally supplemented extension in the same variety of Heyting algebras as the original. We use this tool to investigate a new type of completion of Heyting algebras arising in the context of algebraic proof theory, the so-called hyper-MacNeille completion. We show that the hyper-MacNeille completion of a Heyting algebra is the MacNeille completion of its centrally supplemented extension. This provides an algebraic description of the hyper-MacNeille completion of a Heyting algebra, allows development of further properties of the hyper-MacNeille completion, and provides new examples of varieties of Heyting algebras that are closed under hyper-MacNeille completions. In particular, connections between the centrally supplemented extension and Boolean products allow us to show that any finitely generated variety of Heyting algebras is closed under hyper-MacNeille completions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
