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)
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Abstract

One 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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