Sh:1137

• Fischer, V., & Shelah, S. (2019). The spectrum of independence. Arch. Math. Logic, 58(7-8), 877–884. DOI: 10.1007/s00153-019-00665-y MR: 4003640
• Abstract:
  We study the set of possible size of maximal independent family, to which we refer as spectrum of independence and denote Spec(mi f). We show that: (1) whenever \kappa_1 < \dots < \kappa_n are finitely many regular uncountable cardinals, it is consistent that \{ \kappa_i\}^n_{i = 1} \subseteq Spec (mif); (2) whenever \kappa has uncountable cofinality, it is consistent that Spec(mif) = \{ \aleph_1, \kappa = \mathfrak{c}\}. Assuming large cardinals, in addition to (1) above, we can provide that (\kappa_i, \kappa_{i +1} ) \cap Spec(mif) = \emptyset for each i, 1 \le i < n.
• published version (8p)

@article{Sh:1137,
 author = {Fischer, Vera and Shelah, Saharon},
 title = {{The spectrum of independence}},
 journal = {Arch. Math. Logic},
 fjournal = {Archive for Mathematical Logic},
 volume = {58},
 number = {7-8},
 year = {2019},
 pages = {877--884},
 issn = {0933-5846},
 mrnumber = {4003640},
 mrclass = {03E17 (03E35)},
 doi = {10.1007/s00153-019-00665-y}
}