Some model theoretic ingredients of the proof
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چکیده
Recall that if (K, v) is a valued field, one may consider its completion (K̂, v̂). The extension K̂/K is immediate, i.e. kK = kK̂ and ΓK = ΓK̂ . Definition. • A valued difference field is a structure (K, v, σ), where (K, v) is a valued field and σ is a field endomorphism satisfying σ(x) ∈ OK iff x ∈ OK . It induces a field endomorphism σk on kK and an endomorphism (of ordered abelian groups) σΓ on ΓK .
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