Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-19T00:02:00.763Z Has data issue: false hasContentIssue false
  • English
  • Français

Changing the heights of automorphism towers by forcing with Souslin trees over L

Published online by Cambridge University Press:  12 March 2014

Gunter Fuchs  and
Joel David Hamkins
Gunter Fuchs
Affiliation:
Westfälische Wilhelms-Universität Mùnster, Institut Für Mathematische Logik Und Grundlagenforschung, Einsteinstraβe 62, 48149 Munster., Germany, E-mail: [email protected]
Joel David Hamkins
Affiliation:
Mathematics Program, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016., USA, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid non-isomorphic Souslin trees whose isomorphism relation can be precisely controlled by forcing.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 2 , June 2008 , pp. 614 - 633
Copyright
Copyright © Association for Symbolic Logic 2008

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]Devlin, Keith J. and Johnsbråten, Håvard. The Souslin Problem, Lecture Notes in Mathematics, vol. 405, Springer, Berlin, 1974.CrossRefGoogle Scholar
[2]Fuchs, Gunter and Hamkins, Joel David, Degrees of rigidity for Suslin trees, submitted.Google Scholar
[3]Hamkins, Joel David, Every group has a terminating transfinite automorphism tower. Proceedings of the American Mathematical Society, vol. 126 (1998). no. 11, pp. 3223–3226.CrossRefGoogle Scholar
[4]Hamkins, Joel David, How tall is the automorphism tower of a group?, Logic and Algebra, AMS Contemporary Mathematics Series, vol. 302, 2001, pp. 49–57.Google Scholar
[5]Hamkins, Joel David and Thomas, Simon, Changing the heights of automorphism towers. Annals of Pure and Applied Logic, vol. 102 (2000), no. 1–2, pp. 139–157.CrossRefGoogle Scholar
[6]Thomas, Simon, The automorphism tower problem. Proceedings of the American Mathematical Society, vol. 95 (1985). pp. 166–168.CrossRefGoogle Scholar
[7]Thomas, Simon, The automorphism tower problem II, Israel Journal of Mathematics, vol. 103 (1998), pp. 93–109.CrossRefGoogle Scholar
[8]Thomas, Simon, The Automorphism Tower Problem, to appear.Google Scholar