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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
##### Keywords:
model theory of fields; finite Morley rank; amalgamation; code
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##### References:
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