document: Sigma - admissible families over linear orders Admissible sets of the form HYP -LRB- M -RRB- , where M is a recursively saturated system , are treated . We provide descriptions of subsets M , which are Sigma / sub * / - sets in HYP -LRB- M -RRB- , and of families of subsets M , which form Sigma - regular families in HYP -LRB- M -RRB- , in terms of the concept of being fundamental couched in the article . Fundamental subsets and families are characterized for models of dense linear orderings
doc_bio_tags: O O O O O B I O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I I
extractive_keyphrases: linear orders recursively saturated system fundamental subsets dense linear orderings
abstractive_keyphrases: sigma -admissible families hyp(m)