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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).