Submission date: 30 December 2012.

Abstract:

We construct a computable, computably categorical field of infinite transcendence degree over the rational numbers, using the Fermat polynomials and assorted results from algebraic geometry. We also show that this field has an intrinsically computable (infinite) transcendence basis.

Mathematics Subject Classification: 03C57 (Primary), 03D45, 12L05 (Secondary)

Keywords and phrases:

Full text arXiv 1212.6751: pdf, ps.