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A CLASS OF FIELDS WITH A RESTRICTED MODEL COMPLETENESS PROPERTY

Part of: General field theory Model theory Connections with logic

Published online by Cambridge University Press:  26 March 2021

PHILIP DITTMANN  and
DION LEIJNSE
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
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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.

Keywords

field theorypolynomial idealdiophantine setdefinabilitymodel complete

MSC classification

Primary: 12L12: Model theory
Secondary: 03C10: Quantifier elimination, model completeness and related topics 12E05: Polynomials (irreducibility, etc.)
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 2 , June 2021 , pp. 701 - 708
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Copyright
© The Association for Symbolic Logic 2021

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