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A simple construction for rigid and weakly homogeneous Boolean algebras answering a question of Rubin


Author: Gary Brenner
Journal: Proc. Amer. Math. Soc. 87 (1983), 601-606
MSC: Primary 06E05
DOI: https://doi.org/10.1090/S0002-9939-1983-0687625-3
MathSciNet review: 687625
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Abstract: We introduce a method for constructing Boolean algebras from trees which preserves some of the trees' properties. The method is used to produce a very simple construction for rigid Boolean algebras and to construct a weakly homogeneous Boolean algebra without homogeneous factors.


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

  • [B1] G. Brenner, A new rigid Boolean algebra, Abstracts Amer. Math. Soc. 1 (1980), 389.
  • [B2] -, Tree algebras, Abstracts Amer. Math. Soc. 2 (1981), 270-271.
  • [vD] E. K. van Douwen, An easy compact zero-dimensional rigid space.
  • [vDMR] E. K. van Douwen, J. D. Monk and M. Rubin, Some questions about Boolean algebras, Algebra Universalis 11 (1980), 220-243. MR 588216 (82a:06024)
  • [K] S. Koppelberg, A lattice structure on the isomorphism types of complete Boolean algebras, Set Theory and Model Theory, Proceedings, Bonn 1979, vol, 872, Springer-Verlag, Berlin and New York, 1981, pp. 98-126.
  • [R] M. Rubin, On the reconstruction of Boolean algebras from their automorphism groups, Arch. Math. Logik Grundlag. 20 (1980), 125-146. MR 603333 (82c:06026)
  • [S] R. M. Solovay (unpublished).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0687625-3
Article copyright: © Copyright 1983 American Mathematical Society

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