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Σ12 and Π11 Mad Families

Published online by Cambridge University Press:  12 March 2014

Asger Törnquist*
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark, E-mail: asger@logic.univie.ac.at

Abstract

We answer in the affirmative the following question of Jörg Brendle: If there is a Σ21 mad family, is there then a Π11 mad family?

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2009

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References

REFERENCES

[1] Brendle, Jörg and Khomskii, Yurii, Mad families constructedfrom perfect almost disjoint families, this Journal, vol. 78 (2013), no. 4, pp. 11641180.Google Scholar
[2] Fischer, Vera, Friedman, Sy David, and Zdomskyy, Lyubomyr, Projective wellorders and mad families with large continuum, Annals of Pure and Applied Logic, vol. 162 (2011), no. 11, pp. 853862.Google Scholar
[3] Friedman, Sy-David, Magidor, Menachem, and Woodin, Whugh, Set theory. Abstracts from the workshop held January 9th-January 15th, 2011, Oberwolfach Reports, vol. 8 (2011), no. 1, pp. 85140.Google Scholar
[4] Friedman, Sy-David and Zdomskyy, Lyubomyr, Projective mad families, Annals of Pure and Applied Logic, vol. 161 (2010), no. 12, pp. 15811587.Google Scholar
[5] Mansfield, Richard and Weitkamp, Galen, Recursive aspects of descriptive set theory, Oxford Logic Guides, vol. 11, The Clarendon Press, Oxford University Press, New York, 1985.Google Scholar
[6] Miller, Arnold W., Infinite combinatorics and definability, Annals of Pure and Applied Logic, vol. 41 (1989), no. 2, pp. 179203.Google Scholar