Published May 25, 2018
| Submitted
Journal Article
Open
Definability and almost disjoint families
- Creators
- Törnquist, Asger
Abstract
We show that there are no infinite maximal almost disjoint ("mad") families in Solovay's model, thus solving a long-standing problem posed by A.R.D. Mathias in 1969. We also give a new proof of Mathias' theorem that no analytic infinite almost disjoint family can be maximal, and show more generally that if Martin's Axiom holds at κ<2^(ℵ0), then no κ-Souslin infinite almost disjoint family can be maximal. Finally we show that if ℵ_1^(L[a])<ℵ_1, then there are no Σ^1_2[a] infinite mad families.
Additional Information
© 2018 Elsevier Inc. Received 30 March 2015, Accepted 23 February 2018, Available online 16 March 2018.Attached Files
Submitted - 1503.07577.pdf
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Additional details
- Eprint ID
- 85444
- DOI
- 10.1016/j.aim.2018.03.005
- Resolver ID
- CaltechAUTHORS:20180327-083321909
- Created
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2018-03-27Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field