< I> φ_< sup> 1</sup>< sub> 1</sub>-complete families of elementary sequences

Annals of Pure and Applied Logic 38 (3):257-287 (1988)
Patrick Dehornoy
Université de Caen
If $j$ is an iterable elementary embedding of a model of ZFC into one of its submodels, and, for $\gamma: \omega\to\omega$, one defines $j_\gamma$ to be the sequence whose $n$th entry is the $\gamma(n)$th iterate of $j$, then the family of all sequences $j_\gamma$ is $\Pi_1^1$-complete.
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A Coding of the Countable Linear Orderings.Patrick Dehornoy - 1990 - Studia Logica 49 (4):585 - 590.

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