Geodesic
$\Sigma$-Admissible Families over Linear Orders
Algebra i logika, Tome 41 (2002) no. 2, pp. 228-252.

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Admissible sets of the form $\operatorname{HYP}(\mathfrak M)$, where $\mathfrak M$ is a recursively saturated system, are treated. We provide descriptions of subsets $\mathfrak M$, which are $\Sigma_*$-sets in $\operatorname{HYP}(\mathfrak M)$, and of families of subsets $\mathfrak M$, which form $\Sigma$-regular families in $\operatorname{HYP}(\mathfrak M)$, in terms of the concept of being fundamental couched in the article. Fundamental subsets and families are characterized for models of dense linear orderings.
Keywords: admissible sets, recursively saturated system, $\Sigma$-regular family, fundamental subset. 
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A. I. Stukachev. $\Sigma$-Admissible Families over Linear Orders. Algebra i logika, Tome 41 (2002) no. 2, pp. 228-252. http://geodesic.mathdoc.fr/item/AL_2002_41_2_a7/

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