Dense subtrees in complete Boolean algebras | Zendy

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Dense subtrees in complete Boolean algebras

Author(s) -

König Bernhard

Publication year - 2006

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200510033

Subject(s) - complete boolean algebra , mathematics , boolean algebras canonically defined , free boolean algebra , two element boolean algebra , stone's representation theorem for boolean algebras , interior algebra , boolean algebra , distributivity , homogeneous , ultrafilter , tree (set theory) , filter (signal processing) , discrete mathematics , algebra over a field , combinatorics , pure mathematics , distributive property , algebra representation , jordan algebra , computer science , computer vision

We characterize complete Boolean algebras with dense subtrees. The main results show that a complete Boolean algebra contains a dense tree if its generic filter collapses the algebra's density to its distributivity number and the reverse holds for homogeneous algebras. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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