Abstract
In this paper, we study the relationship between the cofinalityc(Sym(ω)) of the infinite symmetric group and the minimal cardinality\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{b} \) of an unbounded familyF ofω ω.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Blass, A., Shelah, S.: There may be simple\(P_{\aleph _1 } \) and\(P_{\aleph _2 } \)-points and the Rudin-Keisler ordering may be downward directed. Ann. Pure Appl. Logic33, 213–243 (1987)
Booth, D.: Ultrafilters over a countable set. Ann. Math. Logic2, 1–24 (1970)
Canjar, R.M.: Mathias forcing which does not add dominating reals. Proc. Amer. Math. Soc.104, 1239–1248 (1988)
van Douwen, E.: The integers and topology. In: Kunen K., Vaughan J. (eds) Handbook of Set Theoretic Topology, Amsterdam: North-Holland 1984, pp. 111–167
Gregorieff, S.: Combinatorics on ideals and forcing. Ann. Math. Logic3, 363–394 (1971)
Jech, T.: Set theory. New York London: Academic Press 1978
Jech, T.: Multiple Forcing. Cambridge University Press 1986
Kunen, K.: Set Theory. Amsterdam: North-Holland 1980
MacPherson, H.D., Neumann, P.M.: Subgroups of infinite symmetric groups. J. London Math. Soc.42(2), 64–84 (1990)
Sharp, J.D., Thomas, S.: Uniformisation problems and the cofinality of the infinite symmetric group. Preprint (1993)
Shelah, S.: Proper forcing, Lecture Notes in Math. 940. Berlin: Springer 1982
Shelah, S.: On cardinal invariants of the continuum. In: Baumgartner, J., Martin, D.A., Shelah, S. (eds.) Axiomatic set theory. Contemporary Mathematics, vol. 31. AMS, Providence, RI 1984, pp. 183–207
Author information
Authors and Affiliations
Additional information
Research partially supported by NSF Grants
Rights and permissions
About this article
Cite this article
Sharp, J.D., Thomas, S. Unbounded families and the cofinality of the infinite symmetric group. Arch Math Logic 34, 33–45 (1995). https://doi.org/10.1007/BF01269875
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01269875