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<p>We investigate the existence of hybrids of Jonsson theories in various first-order languages. A general framework for hybrids is constructed, defined by ∀∃-sentences true in the Cartesian product of semantic models. For theories in the same language, examples of hybrids are provided; necessary and sufficient conditions for the existence of a hybrid in a functional signature are established; it is shown that a hybrid can inherit properties of the original theories (perfection, categoricity, stability). For theories in different languages, the existence of hybrids is proved for arbitrary enrichments of semantic models to the joint language, and an amalgam is constructed. It is shown that hybrids can differ depending on the enrichments.</p>

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Conditions for Existence of Jonsson Hybrids

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • N. M. Mussina,
  • I. O. Tungushbayeva,
  • A. R. Yeshkeyev

摘要

We investigate the existence of hybrids of Jonsson theories in various first-order languages. A general framework for hybrids is constructed, defined by ∀∃-sentences true in the Cartesian product of semantic models. For theories in the same language, examples of hybrids are provided; necessary and sufficient conditions for the existence of a hybrid in a functional signature are established; it is shown that a hybrid can inherit properties of the original theories (perfection, categoricity, stability). For theories in different languages, the existence of hybrids is proved for arbitrary enrichments of semantic models to the joint language, and an amalgam is constructed. It is shown that hybrids can differ depending on the enrichments.