Boolean algebras with few endomorphisms
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- by Saharon Shelah
- Proc. Amer. Math. Soc. 74 (1979), 135-142
- DOI: https://doi.org/10.1090/S0002-9939-1979-0521887-7
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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
- Matatyahu Rubin, A Boolean algebra with few subalgebras, interval Boolean algebras and retractiveness, Trans. Amer. Math. Soc. 278 (1983), no. 1, 65–89. MR 697061, DOI 10.1090/S0002-9947-1983-0697061-6 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.
Bibliographic Information
- © Copyright 1979 American Mathematical Society
- 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