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Invariance Properties of Almost Disjoint Families

Published online by Cambridge University Press:  12 March 2014

M. Arciga-Alejandre ,
M. Hrušák  and
C. Martinez-Ranero
M. Arciga-Alejandre
Affiliation:
Centro De Investigacion En Matematicas, A.C. Jalisco S/N, Col. Valenciana, Cp 36240 Guanajuato, Gto., Mexico, E-Mail: [email protected]
M. Hrušák
Affiliation:
Centro De Ciencias Matematicas, Universidad Nacional Autonoma De Mexico, A. P. 61 -3 Xangari, C. P. 58089 Morella, Michoacan, Mexico, E-mail: [email protected]
C. Martinez-Ranero
Affiliation:
Centro De Ciencias Matematicas, Universidad Nacional Autonoma De Mexico, A. P. 61 -3 Xangari, C. P. 58089 Morella, Michoacan, Mexico, E-mail: [email protected]
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Abstract

We answer a question of Garcia-Ferreira and Hrušák by consistently constructing a MAD family maximal in the Katětov order. We also answer several questions of Garcia-Ferreira.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 3 , September 2013 , pp. 989 - 999
Copyright
Copyright © Association for Symbolic Logic 2013

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References

REFERENCES

[1] Bartoszyński, T. and Judah, H., Set theory, on the structure of the real line, AK Peters, Wellesley, MA, 1995.Google Scholar
[2] Blass, A., Combinatorial cardinal characteristics of the continuum, Handbook of set theory (Foreman, Matthew and Kanamori, Akihiro, editors), vol. 1, Springer, 2010, pp. 395–489.Google Scholar
[3] Brendle, J., Spinas, O., and Zhang, Y., Uniformity of the meager ideal and maximal cofinitary groups, Journal of Algebra, vol. 232 (2000), pp. 209–225.CrossRefGoogle Scholar
[4] Brendle, J. and Yatabe, S., Forcing indestructibility of MAD families, Annals of Pure and Applied Logic, vol. 132 (2005), no. 2–3, pp. 271–312.CrossRefGoogle Scholar
[5] Cameron, P., Cofinitary permutation groups, Bulletin of the London Mathematical Society, vol. 28 (1996), no. 2, pp. 113–140.CrossRefGoogle Scholar
[6] Garcia-Ferreira, S., Continuous functions between Isbell-Mrowka spaces, Commentationes Mathematicae Universitatis Carolinae, vol. 39 (1998), pp. 185–195.Google Scholar
[7] Garcia-Ferreira, S. and Hrušak, M., Ordering MAD families a la Katětov, this Journal, vol. 68 (2003), no. 4, pp. 1337–1353.Google Scholar
[8] Garcia-Ferreira, S. and Szeptycki, P., MAD families and P-points, Commentationes Mathematicae Universitatis Carolinae, vol. 48 (2007), no. 4, pp. 699–705.Google Scholar
[9] Hrušák, M., Steprans, J., and Zhang, Y., Cofinitary groups, almost disjoint and dominating families, this Journal, vol. 66 (2001), no. 3, pp. 1259–1276.Google Scholar
[10] Hrušák, M. and Zapletal, J., Forcing with quotients, Archive for Mathematical Logic, vol. 47 (2008), no. 7–8, pp. 719–739.Google Scholar
[11] Kastermans, B., Steprans, J., and Zhang, Y., Analytic and coanalytic families of almost disjoint functions, this Journal, vol. 73 (2008), no. 4, pp. 1158–1172.Google Scholar
[12] Raghavan, D. and Steprans, J., On weakly tight families, preprint, 2012.CrossRefGoogle Scholar