A class of fields with a restricted model completeness property

Philip Dittmann; Dion Leijnse

doi:10.1017/jsl.2021.28

A class of fields with a restricted model completeness property

Philip Dittmann, Dion Leijnse

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and in particular obtain a number of new existential (or diophantine) predicates over global fields.

Original language	English
Journal	The Journal of Symbolic Logic
DOIs	https://doi.org/10.1017/jsl.2021.28
Publication status	Published - Jun 2021

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abstract = "We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and in particular obtain a number of new existential (or diophantine) predicates over global fields.",

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AB - We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and in particular obtain a number of new existential (or diophantine) predicates over global fields.

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JO - The Journal of Symbolic Logic

JF - The Journal of Symbolic Logic

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A class of fields with a restricted model completeness property

Abstract

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