# 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)

Bib entry

@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}, doi = {10.1007/s00153-019-00665-y}, mrclass = {03E17 (03E35)}, mrnumber = {4003640}, doi = {10.1007/s00153-019-00665-y} }