# Sh:1090

• Horowitz, H., & Shelah, S. (2019). On the non-existence of mad families. Arch. Math. Logic, 58(3-4), 325–338.
• Abstract:
We show that the non-existence of mad families is equiconsistent with ZFC, answering an old question of Mathias. We also consider the above result in the general context of maximal independent sets in Borel graphs, and we construct a Borel graph G such that ZF + DC+ ’there is no maximal independent set in G’ is equiconsistent with ZFC+ ’there exists an inaccessible cardinal’.
• published version (14p)
Bib entry
@article{Sh:1090,
author = {Horowitz, Haim and Shelah, Saharon},
title = {{On the non-existence of mad families}},
journal = {Arch. Math. Logic},
fjournal = {Archive for Mathematical Logic},
volume = {58},
number = {3-4},
year = {2019},
pages = {325--338},
issn = {0933-5846},
mrnumber = {3928385},
mrclass = {03E35 (03E15 03E25 03E55)},
doi = {10.1007/s00153-018-0640-5},
referred_from_entry = {Contains [Sh:E95a], [Sh:E95b]}
}