Complete ccc Boolean algebras, the order sequential topology, and a problem of von Neumann

0031419 - ÚTIA 2007 RIV GB eng J - Článek v odborném periodiku
Balcar, Bohuslav - Jech, Thomas - Pazák, Tomáš
Complete ccc Boolean algebras, the order sequential topology, and a problem of von Neumann.
[Uplne Booleovy algebry, sekvencialni topologie a von Neumannuv problem.]
Bulletin of the London Mathematical Society. Roč. 37, č. 6 (2005), s. 885-898. ISSN 0024-6093. E-ISSN 1469-2120
Výzkumný záměr: CEZ:AV0Z10750506; CEZ:AV0Z10190503
Klíčová slova: Boolean algebras * Maharam submeasure * weak distributivity * independent reals
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.477, rok: 2005

John von Neumann posed the quetion whether every weakly distributive ccc Boolean algebra have to be a measure algebra. Dorothy Maharam modified the question to submeasurability of the algebra and showed the considtency of negative answer. The article showes the consistency of positive answer, which proves that the assertion is independent on ZFC. There are also several topological reformulations of weak distributivity, a characterization of adding independent reals and some examples.

Clanek obsahuje reseni modifikovane verze von Neumannova-Maharamove problemu z roku 1946.
Trvalý link: http://hdl.handle.net/11104/0132150