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A CLASS OF FIELDS WITH A RESTRICTED MODEL COMPLETENESS PROPERTY
Part of
PHILIP DITTMANN, DION LEIJNSE
Journal:

The Journal of Symbolic Logic / Volume 86 / Issue 2 / June 2021

Published online by Cambridge University Press:

26 March 2021, pp. 701-708

Print publication:

June 2021
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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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A CLASS OF FIELDS WITH A RESTRICTED MODEL COMPLETENESS PROPERTY