On generic automorphisms of a tree structure (New developments of independence notions in model theory)
Hirotaka Kikyo, Akito Tsuboi · Institutional Repositories DataBase (IRDB) · 2010
We give a theory $T$ with the strict order property such that for some auto- morphism $\sigma_{0}$ of a prime model $M_{0}$ of $T$ , the theory $T+\sigma$ is an automorphism" $+\sigma|M_{0}=\sigma_{0}$ " is model complete.Note that $T+\sigma$ is an automorphism" has no model com- panion if $T$ has the strict order property [3].This seems to have some re- semblance with the theory of the rings of Witt Vectors carrying the Frobenius automorphism [1].We consider each natural number $n$ as the set $\{0,1, \ldots, n-1\}$ .Consider a structure $(\Lambda l_{0}, <)$ with $M_{0}=\{f$ : $narrow n+1|n<\omega,$ $f(i)<i+1$ for $i<n\}$ , and $f