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Weak distributivity, a problem of Von Neumann and the mystery of measurability

Bohuslav Balcar & Thomas Jech

Bulletin of Symbolic Logic 12 (2):241-266 (2006)

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Combinatorial dichotomies in set theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.details We give an overview of a research line concentrated on finding to which extent compactness fails at the level of first uncountable cardinal and to which extent it could be recovered on some other perhaps not so large cardinal. While this is of great interest to set theorists, one of the main motivations behind this line of research is in its applicability to other areas of mathematics. We give some details about this and we expose some possible directions for further (...) research. (shrink) Download Export citation Bookmark 5 citations
A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees.Teruyuki Yorioka - 2010 - Annals of Pure and Applied Logic 161 (4):469-487.details We introduce a property of forcing notions, called the anti-, which comes from Aronszajn trees. This property canonically defines a new chain condition stronger than the countable chain condition, which is called the property . In this paper, we investigate the property . For example, we show that a forcing notion with the property does not add random reals. We prove that it is consistent that every forcing notion with the property has precaliber 1 and for forcing notions with the (...) Download Export citation Bookmark 5 citations
On talagrand’s exhaustive pathological submeasure.Omar Selim - 2014 - Journal of Symbolic Logic 79 (4):1046-1060.details Download Export citation Bookmark

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