Depth zero Boolean algebras
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Abstract:
We study the class of depth zero Boolean algebras, both from a classical viewpoint and an effective viewpoint. In particular, we provide an algebraic characterization, constructing an explicit measure for each depth zero Boolean algebra and demonstrating there are no others, and an effective characterization, providing a necessary and sufficient condition for a depth zero Boolean algebra of rank at most $\omega$ to have a computable presentation.References
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Additional Information
- Asher M. Kach
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- Email: kach@math.uconn.edu
- Received by editor(s): June 9, 2008
- Published electronically: March 23, 2010
- Additional Notes: The author thanks his thesis advisor, Steffen Lempp, for all his guidance and suggestions; Christopher Alfeld, Robert Owen, and Daniel Turetsky for numerous conversations, comments, and corrections; and the anonymous referee for his/her comments.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 4243-4265
- MSC (2000): Primary 03D45
- DOI: https://doi.org/10.1090/S0002-9947-10-05002-6
- MathSciNet review: 2608405