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Red fields. (English) Zbl 1127.03032
The authors use a, rather involved, Hrushovski-Fraïssé amalgamation procedure to build a field, necessarily of finite characteristic, which has Morley rank 2 and which contains a definable additive subgroup of rank 1. B. Poizat [J. Symb. Log. 66, 1647–1676 (2001; Zbl 1005.03038)] had constructed a field of rank \(\omega\cdot 2\) with a definable subgroup of rank \(\omega\) and he asked whether there is such a structure of finite rank. The authors note that, more generally, their methods can be used to produce a field of any finite rank \(r\geq 2\) with a definable subgroup of rank \(r-1\).

MSC:
03C60 Model-theoretic algebra
03C50 Models with special properties (saturated, rigid, etc.)
12L12 Model theory of fields
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References:
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