Complete CCC Boolean Algebras, the Order Sequential Topology, and a Problem of Von Neumann | Zendy

Balcar B. | Zendy; Jech T. | Zendy; Pazák T. | Zendy

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Complete CCC Boolean Algebras, the Order Sequential Topology, and a Problem of Von Neumann

Author(s) -

Balcar B.,

Jech T.,

Pazák T.

Publication year - 2005

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609305004807

Subject(s) - mathematics , distributive property , complete boolean algebra , interior algebra , boolean algebras canonically defined , order (exchange) , topological space , algebraic number , discrete mathematics , mathematics subject classification , topology (electrical circuits) , boolean algebra , combinatorics , algebra over a field , pure mathematics , two element boolean algebra , jordan algebra , algebra representation , mathematical analysis , finance , economics

Let B be a complete ccc Boolean algebra and let τ s be the topology on B induced by the algebraic convergence of sequences in B .Either there exists a Maharam submeasure on B or every nonempty open set in ( B , τ s ) is topologically dense. It is consistent that every weakly distributive complete ccc Boolean algebra carries a strictly positive Maharam submeasure. The topological space( B , τ s ) is sequentially compact if and only if the generic extension by B does not add independent reals.Examples are also given of ccc forcings adding a real but not independent reals. 2000 Mathematics Subject Classification 28A60, 06E10 (primary); 03E55, 54A20, 54A25 (secondary).

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