可数无原子布尔代数的泛函约化

Int. J. Algebra Comput. Pub Date : 2022-11-21 DOI:10.1142/s0218196723500078

Bertalan Bodor, Kende Kalina, Csaba A. Szabó

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引用次数: 0

摘要

对于一个代数[公式:见文]，如果每个[公式:见文]是[公式:见文]的项函数，则该代数[公式:见文]被称为函数约简。对可数无原子布尔代数的一阶可互定义的泛函约进行了分类。也就是说，我们认为两个泛函约简是“相同的”，如果它们的自同构群是相同的。我们证明了有13个这样的约简，并描述了它们的结构和自同构群。

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Functional reducts of the countable atomless Boolean algebra

For an algebra [Formula: see text] the algebra [Formula: see text] is called a functional reduct if each [Formula: see text] is a term function of [Formula: see text]. We classify the functional reducts of the countable atomless Boolean algebra up to first-order interdefinability. That is, we consider two functional reducts the “same” if their group of automorphisms is the same. We show that there are 13 such reducts and describe their structures and group of automorphisms.

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Int. J. Algebra Comput.

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