There is a Van Douwen MAD family
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- by Dilip Raghavan PDF
- Trans. Amer. Math. Soc. 362 (2010), 5879-5891 Request permission
Abstract:
We answer a long-standing question of Van Douwen by proving in $\mathrm {ZFC}$ that there is a MAD family of functions in ${\omega }^{\omega }$ that is also maximal with respect to infinite partial functions. In Section 3 we apply the idea of trace introduced in this proof to the still open question of whether analytic MAD families exist in ${\omega }^{\omega }$. Using the idea of trace, we show that any analytic MAD families that may exist in ${\omega }^{\omega }$ must satisfy strong combinatorial constraints. We also show that it is consistent to have MAD families in ${\omega }^{\omega }$ that satisfy these constraints.References
Additional Information
- Dilip Raghavan
- Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
- MR Author ID: 870765
- Email: raghavan@math.toronto.edu
- Received by editor(s): July 22, 2008
- Published electronically: June 11, 2010
- Additional Notes: The author was partially supported by NSF Grant DMS-0456653.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 5879-5891
- MSC (2010): Primary 03E17, 03E15, 03E05, 03E50
- DOI: https://doi.org/10.1090/S0002-9947-2010-04975-X
- MathSciNet review: 2661500