Journal of Symbolic Logic

Effective Presentability of Boolean Algebras of Cantor-Bendixson Rank 1

Rod Downey and Carl G. Jockusch, Jr.

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Abstract

We show that there is a computable Boolean algebra $\mathscr{B}$ and a computably enumerable ideal I of $\mathscr{B}$ such that the quotient algebra $\mathscr{B}/I$ is of Cantor-Bendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even though Feiner's construction yields a Boolean algebra of infinite Cantor-Bendixson rank.

Article information

Source
J. Symbolic Logic, Volume 64, Issue 1 (1999), 45-52.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745690

Mathematical Reviews number (MathSciNet)
MR1683893

Zentralblatt MATH identifier
0924.03084

JSTOR
links.jstor.org

Citation

Downey, Rod; Jockusch, Carl G. Effective Presentability of Boolean Algebras of Cantor-Bendixson Rank 1. J. Symbolic Logic 64 (1999), no. 1, 45--52. https://projecteuclid.org/euclid.jsl/1183745690


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