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Preprint Number 594

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594. Kirsten Eisentraeger and Alexandra Shlapentokh
Hilbert's Tenth Problem over Function Fields of Positive Characteristic
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Submission date: 11 June 2013.

Abstract:

We prove that the existential theory of any function field K of characteristic p> 0 is undecidable in the language of rings provided that the constant field does not contain the algebraic closure of a finite field. We also extend the undecidability proof for function fields of higher transcendence degree to characteristic 2 and show that the first-order theory of any function field of positive characteristic is undecidable in the language of rings without parameters.

Mathematics Subject Classification: 03C07, 03D35, 11U05

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Full text arXiv 1306.2669: pdf, ps.


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