Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T15:24:02.775Z Has data issue: false hasContentIssue false
  • English
  • Français

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: arciga@cimat.mx
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: michael@matmor.unam.mx
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: azarel@matmor.unam.mx
Get access Rights & Permissions [Opens in a new window]

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

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] 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