There is a Van Douwen MAD family

Author:
Dilip Raghavan

Journal:
Trans. Amer. Math. Soc. **362** (2010), 5879-5891

MSC (2010):
Primary 03E17, 03E15, 03E05, 03E50

Published electronically:
June 11, 2010

MathSciNet review:
2661500

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Abstract | References | Similar Articles | Additional Information

Abstract: We answer a long-standing question of Van Douwen by proving in that there is a MAD family of functions in 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 . Using the idea of trace, we show that any analytic MAD families that may exist in must satisfy strong combinatorial constraints. We also show that it is consistent to have MAD families in that satisfy these constraints.

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Additional Information

**Dilip Raghavan**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4

Email:
raghavan@math.toronto.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-2010-04975-X

Keywords:
Maximal almost disjoint family,
cardinal invariants,
analytic set

Received by editor(s):
July 22, 2008

Published electronically:
June 11, 2010

Additional Notes:
The author was partially supported by NSF Grant DMS-0456653.

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.