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 and are structure diagrams for primitive Boolean algebras, call a homomorphism from onto *right-strong* iff whenever , there is an such that and ; let *RSE* denote the category of diagrams and onto right-strong homomorphisms. The relation `` structures '' 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 structures a Boolean algebra recursive in .

**[1]**William Hanf,*Primitive Boolean algebras*, Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1974, pp. 75–90. MR**0379182****[2]**R. S. Pierce,*Compact zero-dimensional metric spaces of finite type*, American Mathematical Society, Providence, R.I., 1972. Memoirs of the American Mathematical Society, No. 130. MR**0357268**

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0357269-7

Article copyright:
© Copyright 1975
American Mathematical Society