Diophantine relations between rings of s-integers of fields of algebraic functions in one variable over constant fields of positive characteristic
Journal of Symbolic Logic 58 (1):158-192 (1993)
AbstractOne of the main theorems of the paper states the following. Let R-K-M be finite extensions of a rational one variable function field R over a finite field of constants. Let S be a finite set of valuations of K. Then the ring of elements of K having no poles outside S has a Diophantine definition over its integral closure in M
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First-order definitions of rational functions and S -integers over holomorphy rings of algebraic functions of characteristic 0.Alexandra Shlapentokh - 2005 - Annals of Pure and Applied Logic 136 (3):267-283.
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