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Abstract:

We give an example of a parameter-free definable henselian valuation ring which is neither definable by a parameter-free ∀∃-formula nor by a parameter-free ∃∀-formula in the language of rings. This answers a question of Prestel.

Mathematics Subject Classification: Primary: 03C40, 12L12. Secondary: 12E30, 13J15

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Full text arXiv 1504.01871: pdf, ps.