Geodesic
On initial segments of degrees of constructibility
Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 939-946 
V. G. Kanovei. On initial segments of degrees of constructibility. Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 939-946. http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a11/
@article{MZM_1975_17_6_a11,
     author = {V. G. Kanovei},
     title = {On initial segments of degrees of constructibility},
     journal = {Matemati\v{c}eskie zametki},
     pages = {939--946},
     year = {1975},
     volume = {17},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a11/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathfrak{M}$ be a fixed countable standard transitive model of $ZF+V=L$. We consider the structure Mod of degrees of constructibility of real numbers x with respect to $\mathfrak{M}$ such that $\mathfrak{M}$ (x) is a model. An initial segment $Q\subseteq\operatorname{Mod}$ is called realizable if some extension of $\mathfrak{M}$ with the same ordinals contains exclusively the degrees of constructibility of real numbers from $Q$ (and is a model of $ZFC$). We prove the following: if $Q$ is a realizable initial segment, then $\exists\,x\ [\forall\,y\ [x\in\operatorname{Mod}\&[y\in Q\to y.