Anote on elimination of imaginaries for pairs of fields


We show that, if B is a field and A \neq B is any algebraically closed  field extension of B, then the theory of (A,B) eliminates imaginaries if  and only if A is a finite extension of B (and so if and only if (A,B)  is elementary equivalent to  ( \mathbb{C}, \mathbb{R})).

DOI Code: 10.1285/i15900932v22n1p89

Keywords: Elimination of imaginaries; Pair of fields

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