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

  • Gunter Fuchs (a1) and Joel David Hamkins (a2)
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.

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References
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[1]Devlin, Keith J. and Johnsbråten, Håvard. The Souslin Problem, Lecture Notes in Mathematics, vol. 405, Springer, Berlin, 1974.
[2]Fuchs, Gunter and Hamkins, Joel David, Degrees of rigidity for Suslin trees, submitted.
[3]Hamkins, Joel David, Every group has a terminating transfinite automorphism tower. Proceedings of the American Mathematical Society, vol. 126 (1998). no. 11, pp. 32233226.
[4]Hamkins, Joel David, How tall is the automorphism tower of a group?, Logic and Algebra, AMS Contemporary Mathematics Series, vol. 302, 2001, pp. 4957.
[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. 139157.
[6]Thomas, Simon, The automorphism tower problem. Proceedings of the American Mathematical Society, vol. 95 (1985). pp. 166168.
[7]Thomas, Simon, The automorphism tower problem II, Israel Journal of Mathematics, vol. 103 (1998), pp. 93109.
[8]Thomas, Simon, The Automorphism Tower Problem, to appear.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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