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<p>We examine how elementary classes of algebras can be represented as reducts of logically simpler classes. For example, we demonstrate that every elementary class is a reduct of a positive class, and that any variety is a reduct of a four-based variety. Additionally, we introduce hierarchies based on fragments of first-order logic to analyse these reducts, providing a more detailed structural understanding of the landscape of algebraic classes.</p>

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Logical complexity of reducts of elementary algebraic classes

  • 期刊论文

  • 发表日期：

    2025年12月14日

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  • Carles Cardó

摘要

We examine how elementary classes of algebras can be represented as reducts of logically simpler classes. For example, we demonstrate that every elementary class is a reduct of a positive class, and that any variety is a reduct of a four-based variety. Additionally, we introduce hierarchies based on fragments of first-order logic to analyse these reducts, providing a more detailed structural understanding of the landscape of algebraic classes.