Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T21:24:38.515Z Has data issue: false hasContentIssue false

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: [email protected]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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