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<p>I study definability notions in the framework of affine continuous logic. Some general results concerning types and definable relations in affinely complete theories are proved. If the theory has a first order model, its extremal theory is a complete first order theory and first order definable sets are affinely definable. If it has a compact model, definable sets are exactly the end-sets of definable predicates. As an example, it is proved in the theory of probability algebras that one dimensional definable sets are exactly the intervals [<i>a</i>,&#xa0;<i>b</i>].</p>

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Definability in affine logic

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  • 发表日期：

    2025年4月25日

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  • Seyed-Mohammad Bagheri

摘要

I study definability notions in the framework of affine continuous logic. Some general results concerning types and definable relations in affinely complete theories are proved. If the theory has a first order model, its extremal theory is a complete first order theory and first order definable sets are affinely definable. If it has a compact model, definable sets are exactly the end-sets of definable predicates. As an example, it is proved in the theory of probability algebras that one dimensional definable sets are exactly the intervals [a, b].