Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T01:43:57.756Z Has data issue: false hasContentIssue false
  • English
  • Français

The canary tree revisited

Published online by Cambridge University Press:  12 March 2014

Tapani Hyttinen  and
Mika Rautila
Tapani Hyttinen
Affiliation:
Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail: [email protected], E-mail: [email protected]
Mika Rautila
Affiliation:
Department of Mathematics, P.O. BOX 4, 00014 University of Helsinki, Finland, E-mail: [email protected], E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract.

We generalize the result of Mekler and Shelah [3] that the existence of a canary tree is independent of ZFC + GCH to uncountable regular cardinals. We also correct an error from the original proof.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 4 , December 2001 , pp. 1677 - 1694
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]Goldstern, Martin, Tools for your forcing construction. Set theory of the reals (Ramat Gait, 1991), Bar-Ilan University, Ramat Gan, 1993, pp. 305–360.Google Scholar
[2]Huuskonen, Taneli, Hyttinen, Tapani, and Rautila, Mika, On the κ-cub game on λ and i[λ]Archive for Mathematical Logic, (1999), pp. 549–557.Google Scholar
[3]Mekler, Alan H. and Shelah, Saharon, The canary tree, Canadian Mathematical Bulletin, vol. 36 (1993), no. 2, pp. 209–215.CrossRefGoogle Scholar
[4]Shelah, S. and Stanley, L., Generalized Martins axiom and Souslin's hypothesis, Israel Journal of Mathematics, vol. 43 (1982), no. 3, pp. 225–236.CrossRefGoogle Scholar
[5]Shelah, Saharon, On successors of singular cardinals, Logic colloquium ′78 (M Boffa, D. van Dalen, and K. McAloon, editors), Studies in Logic and Foundations of Mathematics, vol. 97, North-Holland, 1979.Google Scholar
[6]Shelah, Saharon, Reflecting stationary sets and successors of singular cardinals. Archive for Mathematical Logic,vol. 31 (1991), pp. 25–53.CrossRefGoogle Scholar
[7]Shelah, Saharon, Proper and improper forcing, 2ed., Springer-Verlag, Berlin, 1998.CrossRefGoogle Scholar
[8]Shelah, Saharon, Not collapsing cardinals ≤ κ in (< κ)-support iterations, Israel Journal of Mathematics, (accepted).Google Scholar
[9]Väänänen, Jouko, Games and trees in infinitary logic: a survey. Quantifiers: Logics, models, and computation (M. Krynick et al, editor), vol. I, Kluwer Academic Publishers, 1995, pp. 105–138.CrossRefGoogle Scholar