Submission date: 8 November 2019

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.

Mathematics Subject Classification: 12L12 (Primary) 03C10, 12E05 (Secondary)

Keywords and phrases:

Full text arXiv 1911.03202: pdf, ps.