Globally valued function fields: existential closure

Itaï Ben Yaacov; Ehud Hrushovski

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arXiv · 2212.07269

Globally valued function fields: existential closure

Itaï Ben Yaacov·Ehud Hrushovski

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Abstract

These notes form part of a joint research project on the logic of fields with many valuations, connected by a product formula. We define such structures and name them {\em globally valued fields} (GVFs). This text aims primarily at a proof that {\em the canonical GVF structure on $k(t)^{alg}$ is existentially closed}. This can be read as saying that a variety {\em with a distinguished curve class} is a good approximation for a formula in the language of GVFs, in the same way that a variety is close to a formula for the theory ACF of algebraically closed fields.

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BibTeX RIS

Itaï Ben Yaacov, Ehud Hrushovski. 2022-12-14. Globally valued function fields: existential closure. https://arxiv.org/abs/2212.07269

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