On the triple jump of the set of atoms of a Boolean algebra

Author:
Antonio Montalbán

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2589-2595

MSC (2000):
Primary 03D80

Published electronically:
March 11, 2008

MathSciNet review:
2390531

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the following result concerning the degree spectrum of the atom relation on a computable Boolean algebra. Let be a computable Boolean algebra with infinitely many atoms and be the Turing degree of the atom relation of . If is a c.e. degree such that , then there is a computable copy of where the atom relation has degree . In particular, for every c.e. degree , any computable Boolean algebra with infinitely many atoms has a computable copy where the atom relation has degree .

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Additional Information

**Antonio Montalbán**

Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637

Email:
antonio@mcs.vuw.ac.nz

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09248-4

Keywords:
Boolean algebra,
atom,
relation,
degree spectrum

Received by editor(s):
December 8, 2006

Received by editor(s) in revised form:
April 12, 2007, April 22, 2007, and May 31, 2007

Published electronically:
March 11, 2008

Additional Notes:
This research was partially supported by NSF Grant DMS-0600824 and by the Marsden Foundation of New Zealand, via a postdoctoral fellowship.

Communicated by:
Julia Knight

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.