A class of fields with a restricted model completeness property
Philip Dittmann, Dion Leijnse
TL;DR
This paper introduces a new class of fields characterized by a restricted model completeness property, providing new existential definability results over global fields.
Contribution
It defines and characterizes a natural class of fields with restricted model completeness, including global fields, and derives new existential predicates for them.
Findings
Global fields belong to this class.
New existential (Diophantine) predicates over global fields.
Characterization of the class by equivalent conditions.
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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