Skip to main content Accessibility help

Cofinitary groups, almost disjoint and dominating families

  • Michael Hrušák (a1), Juris Steprans (a2) and Yi Zhang (a3)


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 .


Corresponding author

Current address: Department of Mathematics and Computer Science, Istanbul Bilgi University, Kustepe, Istanbul, 80310, Turkey, E-mail:


Hide All
[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. 169178.
[2]Baumgartner, J. E. and Laver, R., Iterated perfect–set forcing, Annals of Mathematical Logic, vol. 17 (1979), pp. 271288.
[3]Cameron, P. J., Cofinitary permutation groups, Bulletin of the London Mathematical Society, vol. 28 (1996), pp. 113140.
[4]Jech, T., Set theory, Academic Press, 1978.
[5]Kunen, K., Set theory, an introduction to independence proofs, North-Holland, Amsterdam, 1980.
[6]Miller, A., Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), no. 1, pp. 93114.
[7]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, 1982.
[8]Spinas, O. and Shelah, S., The distributivity numbers of ℘(ω)/f in and its square, (preprint).
[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. 335351.
[10]van Douwen, E., The integers and topology, Handbook of set theoretic topology (Kunen, K. and Vaughan, J., editors), North-Holland, Amsterdam, 1984, pp. 111167.
[11]Zhang, Y., Cofinitary groups and almost disjoint families, Ph.D. thesis, Rutgers University, 1997.
[12]Zhang, Y., On a class of mad families, this Journal, vol. 64 (1999), no. 2, pp. 737746.
[13]Zhang, Y., Maximal cofinitary groups, Archive of Mathematical Logic, vol. 39 (2000), pp. 4152.
[14]Zhang, Y., Permutation groups and covering properties, Journal of London Mathematical Society, vol. 63 (2001), no. 2, pp. 115.

Related content

Powered by UNSILO

Cofinitary groups, almost disjoint and dominating families

  • Michael Hrušák (a1), Juris Steprans (a2) and Yi Zhang (a3)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.