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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

$\omega !$ can be a nontrivial automorphism group


Author: Judith Roitman
Journal: Proc. Amer. Math. Soc. 112 (1991), 623-628
MSC: Primary 03E35; Secondary 03E05, 06E05, 20B27
DOI: https://doi.org/10.1090/S0002-9939-1991-1059636-4
MathSciNet review: 1059636
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Abstract: Under the axiom "there are ${\omega _1}$ cofinal Cohen reals," the symmetric group on $\omega$ is the nontrivial automorphism group of a thin-tall superatomic Boolean algebra. Certain product groups are also, under the same axiom, nontrivial automorphism groups of thin-tall superatomic Boolean algebras.


References [Enhancements On Off] (What's this?)

  • Alan Dow and Peter Simon, Thin-tall Boolean algebras and their automorphism groups, Algebra Universalis 29 (1992), no. 2, 211–226. MR 1157434, DOI https://doi.org/10.1007/BF01190607
  • Judy Roitman, Superatomic Boolean algebras, Handbook of Boolean algebras, Vol. 3, North-Holland, Amsterdam, 1989, pp. 719–740. MR 991608
  • ---, Uncountable autohomeomorphism groups of thin-tall locally compact scattered spaces, preprint.

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Article copyright: © Copyright 1991 American Mathematical Society