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

Keywords and phrases:

Full text arXiv 1306.2669: pdf, ps.