Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-04-30T12:41:14.867Z Has data issue: false hasContentIssue false
  • English
  • Français

Cofinitary groups, almost disjoint and dominating families

Published online by Cambridge University Press:  12 March 2014

Michael Hrušák ,
Juris Steprans  and
Yi Zhang
Michael Hrušák
Affiliation:
Mathematics Department, York University, 4700 Keele Street, North York, Ontario, CanadaM3J 1P3, E-mail: yu50029@pascal.math.yorku.ca
Juris Steprans
Affiliation:
Mathematics Department, York University, 4700 Keele Street, North York, Ontario, CanadaM3J 1P3, E-mail: steprans@mathstat.yorku.ca
Yi Zhang*
Affiliation:
Mathematics Institute, Academia Sinica, Beijing, 100080, P. R. China
*
Current address: Department of Mathematics and Computer Science, Istanbul Bilgi University, Kustepe, Istanbul, 80310, Turkey, E-mail: zhang@bilgi.edu.tr
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we show that it is consistent with ZFC that the cardinality of every maximal cofinitary group of Sym(ω) is strictly greater than the cardinal numbers and .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1259 - 1276
Copyright
Copyright © Association for Symbolic Logic 2001

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]Adeleke, S. A., Embeddings of infinite permutation groups in sharp, highly transitive, and homogeneous groups, Proceedings of Edinburgh Mathematical Society, vol. 31 (1981), pp. 169–178.CrossRefGoogle Scholar
[2]Baumgartner, J. E. and Laver, R., Iterated perfect–set forcing, Annals of Mathematical Logic, vol. 17 (1979), pp. 271–288.CrossRefGoogle Scholar
[3]Cameron, P. J., Cofinitary permutation groups, Bulletin of the London Mathematical Society, vol. 28 (1996), pp. 113–140.CrossRefGoogle Scholar
[4]Jech, T., Set theory, Academic Press, 1978.Google Scholar
[5]Kunen, K., Set theory, an introduction to independence proofs, North-Holland, Amsterdam, 1980.Google Scholar
[6]Miller, A., Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), no. 1, pp. 93–114.CrossRefGoogle Scholar
[7]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, 1982.CrossRefGoogle Scholar
[8]Spinas, O. and Shelah, S., The distributivity numbers of ℘(ω)/f in and its square, (preprint).Google Scholar
[9]Truss, J. K., Embeddings of infinite permutation groups, Proceedings of groups–St Andrews 1985 (Robertson, E. F. and Cambell, C. M., editors), London Mathematical Society Lecture Note Series, vol. 121, Cambridge University Press, 1986, pp. 335–351.Google Scholar
[10]van Douwen, E., The integers and topology, Handbook of set theoretic topology (Kunen, K. and Vaughan, J., editors), North-Holland, Amsterdam, 1984, pp. 111–167.CrossRefGoogle Scholar
[11]Zhang, Y., Cofinitary groups and almost disjoint families, Ph.D. thesis, Rutgers University, 1997.Google Scholar
[12]Zhang, Y., On a class of mad families, this Journal, vol. 64 (1999), no. 2, pp. 737–746.Google Scholar
[13]Zhang, Y., Maximal cofinitary groups, Archive of Mathematical Logic, vol. 39 (2000), pp. 41–52.CrossRefGoogle Scholar
[14]Zhang, Y., Permutation groups and covering properties, Journal of London Mathematical Society, vol. 63 (2001), no. 2, pp. 1–15.CrossRefGoogle Scholar