, Volume 79, Issue 2-3, pp 129-151

Strongly minimal expansions of algebraically closed fields

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Abstract

(1) We construct a strongly minimal expansion of an algebraically closed field of a given characteristic. Actually we show a much more general result, implying for example the existence of a strongly minimal set with two different field structures of distinct characteristics.

(2) A strongly minimal expansion of an algebraically closed field that preserves the algebraic closure relation must be an expansion by (algebraic) constants.

Supported by NSF grants DMS 8903378.