Geodesic
Definability of boolean algebras in $\mathbb{HF}$-superstrustures
Algebra i logika, Tome 39 (2000) no. 6, pp. 711-719 
A. V. Romina. Definability of boolean algebras in $\mathbb{HF}$-superstrustures. Algebra i logika, Tome 39 (2000) no. 6, pp. 711-719. http://geodesic.mathdoc.fr/item/AL_2000_39_6_a4/
@article{AL_2000_39_6_a4,
     author = {A. V. Romina},
     title = {Definability of boolean algebras in $\mathbb{HF}$-superstrustures},
     journal = {Algebra i logika},
     pages = {711--719},
     year = {2000},
     volume = {39},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2000_39_6_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Within the frames of the $\Sigma$-definability approach propounded by Yu. L. Ershov, we study into the definability of Boolean algebras and their Frechet ranks in hereditarily finite superstructures. Examples are constructed of a superatomic Boolean algebra whose Frechet rank is not $\Sigma$-definable in the hereditarily finite superstructure over that algebra, and of an admissible set in which the atomless Boolean algebra is not autostable.