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”.
Original language | English |
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Pages (from-to) | 325-338 |
Number of pages | 14 |
Journal | Archive for Mathematical Logic |
Volume | 58 |
Issue number | 3-4 |
DOIs | |
State | Published - 9 May 2019 |
Bibliographical note
Publisher Copyright:© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
Keywords
- Amalgamation
- Borel graphs
- Forcing
- Inaccessible cardinals
- Mad families