Kirsten Eisentraeger, Alexandra Shlapentokh
Published 2007-09-12, updated 2008-02-27Version 2
We prove that the first-order theory of any function field K of characteristic p>2 is undecidable in the language of rings without parameters. When K is a function field in one variable whose constant field is algebraic over a finite field, we can also prove undecidability in characteristic 2. The proof uses a result by Moret-Bailly about ranks of elliptic curves over function fields.
Comments: 12 pages; strengthened main theorem, proved undecidability in the language of rings without parameters
Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields
Hilbert's Tenth Problem over Function Fields of Positive Characteristic Not Containing the Algebraic Closure of a Finite Field
First-order definitions in function fields over anti-Mordellic fields
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