A definable henselian valuation with high quantifier complexity
classification
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definableparameter-freeexistsforallformulahenselianvaluationanswers
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We give an example of a parameter-free definable henselian valuation ring which is neither definable by a parameter-free $\forall\exists$-formula nor by a parameter-free $\exists\forall$-formula in the language of rings. This answers a question of Prestel.
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