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Effective presentability of Boolean algebras of Cantor-Bendixson rank 1

Published online by Cambridge University Press:  12 March 2014

Rod Downey
Affiliation:
Department of Mathematics, Victoria University of Wellington, Department of Mathematics, Wellington, New Zealand E-mail: rod.downey@vuw.ac.nz
Carl G. Jockusch Jr.
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Il 61801–2917, USA E-mail: jockusch@math.uiuc.edu

Abstract

We show that there is a computable Boolean algebra and a computably enumerable ideal I of such that the quotient algebra /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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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