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Preprint Number 632

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632. Jochen Koenigsmann
On a question of Abraham Robinson's

Submission date: 27 September 2013.


In this note we give a negative answer to Abraham Robinson's question whether a finitely generated extension of an undecidable field is always undecidable. We construct 'natural' undecidable fields of transcendence degree 1 over Q all of whose proper finite extensions are decidable. We also construct undecidable algebraic extensions of Q that allow decidable finite extensions.

Mathematics Subject Classification: 12L05, 12E30

Keywords and phrases:

Full text arXiv 1309.7138: pdf, ps.

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