On the expressive power of quantifiers in continuous logic

Itaï Ben Yaacov

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arXiv · 2207.01863

On the expressive power of quantifiers in continuous logic

Itaï Ben Yaacov

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Abstract

In this short note we compare the expressive power of real-valued continuous logic (or just continuous logic, in recent literature) with that of compact-valued continuous logic, proposed by Chang and Keisler. We conclude that the two logics have the same expressive power, and moreover, that this remains true if we replace the plethora of potential quantifiers of compact-valued logic with a single ''primordial'' one.

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Itaï Ben Yaacov. 2022-07-05. On the expressive power of quantifiers in continuous logic. https://arxiv.org/abs/2207.01863

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