Title: $\Sigma$-Admissible Families over Linear Orders
Abstract: Admissible sets of the form
${\rm HYP}({\mathfrak M})$, where ${\mathfrak M}$ is a
recursively saturated system, are treated. We provide
descriptions of subsets ${\mathfrak M}$, which are
$\Sigma_*$-sets in ${\rm HYP}({\mathfrak M})$, and of
families of subsets ${\mathfrak M}$, which form
$\Sigma$-regular families in ${\rm HYP}({\mathfrak M})$,
in terms of the concept of being fundamental couched
in the article. Fundamental subsets and families are
characterized for models of dense linear orderings.
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