# Sh:1137

• Fischer, V., & Shelah, S. (2019). The spectrum of independence. Arch. Math. Logic, 58(7-8), 877–884.
• 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},
mrnumber = {4003640},
mrclass = {03E17 (03E35)},
doi = {10.1007/s00153-019-00665-y}
}