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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Stukachyov, A.I. Σ-Admissible Families over Linear Orders. Algebra and Logic 41, 127–139 (2002). https://doi.org/10.1023/A:1015312831772
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DOI: https://doi.org/10.1023/A:1015312831772