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Structure diagrams for primitive Boolean algebras


Author: James Williams
Journal: Proc. Amer. Math. Soc. 47 (1975), 1-9
DOI: https://doi.org/10.1090/S0002-9939-1975-0357269-7
MathSciNet review: 0357269
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Abstract | References | Additional Information

Abstract: If $ S$ and $ T$ are structure diagrams for primitive Boolean algebras, call a homomorphism $ f$ from $ S$ onto $ T$ right-strong iff whenever $ xTf(t)$, there is an $ s$ such that $ f(s) = x$ and $ sSt$; let RSE denote the category of diagrams and onto right-strong homomorphisms. The relation ``$ S$ structures $ \mathfrak{B}$'' between diagrams and Boolean algebras induces a 1-1 correspondence between the components of RSE and the isomorphism types of primitive Boolean algebras. Up to isomorphism, each component of RSE contains a unique minimal diagram and a unique maximal tree diagram. The minimal diagrams are like those given in a construction by William Hanf. The construction which is given for producing maximal tree diagrams is recursive; as a result, every diagram $ S$ structures a Boolean algebra recursive in $ S$.


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

  • [1] William Hanf, Primitive Boolean algebras, Proc. Sympos. Pure Math., vol. 25, Amer. Math. Soc., Providence, R. I., 1974, pp. 75-90. MR 0379182 (52:88)
  • [2] R. S. Pierce, Compact zero-dimensional metric spaces of finite type, Mem. Amer. Math. Soc. No. 130 (1970). MR 0357268 (50:9736)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0357269-7
Article copyright: © Copyright 1975 American Mathematical Society

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