Downward closure of depth in countable Boolean algebras

Downward closure of depth in countable Boolean algebras

We study the set of depths of relative algebras of countable Boolean algebras, in particular the extent to which this set may not be downward closed within the countable ordinals for a fixed countable Boolean algebra. Doing so, we exhibit a structural difference between the class of arbitrary rank c...

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Veröffentlicht in:Algebra universalis 2012-10, Vol.68 (1-2), p.57-74
Hauptverfasser: Kach, Asher M., Lempp, Steffen
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematics
Mathematics and Statistics
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Zusammenfassung:We study the set of depths of relative algebras of countable Boolean algebras, in particular the extent to which this set may not be downward closed within the countable ordinals for a fixed countable Boolean algebra. Doing so, we exhibit a structural difference between the class of arbitrary rank countable Boolean algebras and the class of rank one countable Boolean algebras.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-012-0188-x