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Boolean algebras with few endomorphisms


Author: Saharon Shelah
Journal: Proc. Amer. Math. Soc. 74 (1979), 135-142
MSC: Primary 06E05; Secondary 03E35, 03G05
DOI: https://doi.org/10.1090/S0002-9939-1979-0521887-7
MathSciNet review: 521887
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Abstract: Using diamond for $ {\aleph _1}$ we construct a Boolean algebra in $ {\aleph _1}$, whose only endomorphisms are those definable using finitely many elements and ultrafilters. We also generalize Rubin's construction to higher cardinals.


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

  • [R] M. Rubin, On Boolean algebra with few endomorphisms, Trans. Amer. Math. Soc. (to appear). MR 697061 (85a:06024)
  • [Sh1] S. Shelah, Models with second order properties. III, Omitting types for $ L(Q)$ in higher cardinals, Proc. Sympos. Model Theory (West Berlin 1977), Edited by K. Makowski, Arch. Math. Logik Grundlagenforsch.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0521887-7
Keywords: Boolean algebra, endomorphism
Article copyright: © Copyright 1979 American Mathematical Society

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