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A CLASS OF FIELDS WITH A RESTRICTED MODEL COMPLETENESS PROPERTY

Published online by Cambridge University Press:  26 March 2021

PHILIP DITTMANN
Affiliation:
INSTITUT FÜR ALGEBRA TU DRESDEN, DRESDEN, GERMANYE-mail:philip.dittmann@tu-dresden.de
DION LEIJNSE
Affiliation:
RADBOUD UNIVERSITEIT NIJMEGEN NIJMEGEN, THE NETHERLANDSE-mail:d.leijnse@gmail.com

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.

Type
Article
Copyright
© The Association for Symbolic Logic 2021

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