First-order definitions of rational functions and S -integers over holomorphy rings of algebraic functions of characteristic 0

Annals of Pure and Applied Logic 136 (3):267-283 (2005)
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Abstract

We consider the problem of constructing first-order definitions in the language of rings of holomorphy rings of one-variable function fields of characteristic 0 in their integral closures in finite extensions of their fraction fields and in bigger holomorphy subrings of their fraction fields. This line of questions is motivated by similar existential definability results over global fields and related questions of Diophantine decidability

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10.1016/j.apal.2005.04.004

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Definability and decision problems in arithmetic.Julia Robinson - 1949 - Journal of Symbolic Logic 14 (2):98-114.
Questions of decidability and undecidability in number theory.B. Mazur - 1994 - Journal of Symbolic Logic 59 (2):353-371.
Defining transcendentals in function fields.Jochen Koenigsmann - 2002 - Journal of Symbolic Logic 67 (3):947-956.
Indécidabilité Des corps de courbe réelle.Luc Bélair & Jean-Louis Duret - 1994 - Journal of Symbolic Logic 59 (1):87-91.

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