Changing cofinality of a measurable cardinal (An alternative proof)
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Displaying 1 – 11 of 11
Changing cofinality of cardinals
Menachem Magidor (1978)
Fundamenta Mathematicae
Changing measurable into accessible cardinals [Book]
K. L. Prikry (1970)
Closed discrete subsets of separable spaces and relative versions of normality, countable paracompactness and property
Samuel Gomes da Silva (2011)
Commentationes Mathematicae Universitatis Carolinae
In this paper we show that a separable space cannot include closed discrete subsets which have the cardinality of the continuum and satisfy relative versions of any of the following topological properties: normality, countable paracompactness and property . It follows that it is consistent that closed discrete subsets of a separable space which are also relatively normal (relatively countably paracompact, relatively ) in are necessarily countable. There are, however, consistent examples of...
Colimit-dense subcategories
Jiří Adámek, Andrew D. Brooke-Taylor, Tim Campion, Leonid Positselski, Jiří Rosický (2019)
Commentationes Mathematicae Universitatis Carolinae
Among cocomplete categories, the locally presentable ones can be defined as those with a strong generator consisting of presentable objects. Assuming Vopěnka’s Principle, we prove that a cocomplete category is locally presentable if and only if it has a colimit dense subcategory and a generator consisting of presentable objects. We further show that a -element set is colimit-dense in , and spaces of countable dimension are colimit-dense in .
Condensation and large cardinals
Sy-David Friedman, Peter Holy (2011)
Fundamenta Mathematicae
We introduce two generalized condensation principles: Local Club Condensation and Stationary Condensation. We show that while Strong Condensation (a generalized condensation principle introduced by Hugh Woodin) is inconsistent with an ω₁-Erdős cardinal, Stationary Condensation and Local Club Condensation (which should be thought of as weakenings of Strong Condensation) are both consistent with ω-superstrong cardinals.
Consistency of the Silver dichotomy in generalised Baire space
Sy-David Friedman (2014)
Fundamenta Mathematicae
Silver’s fundamental dichotomy in the classical theory of Borel reducibility states that any Borel (or even co-analytic) equivalence relation with uncountably many classes has a perfect set of classes. The natural generalisation of this to the generalised Baire space for a regular uncountable κ fails in Gödel’s L, even for κ-Borel equivalence relations. We show here that Silver’s dichotomy for κ-Borel equivalence relations in for uncountable regular κ is however consistent (with GCH), assuming...
Continuity of characters in products of algebras
Angel Rafael Larotonda, Ignacio M. Zalduendo (1983)
Commentationes Mathematicae Universitatis Carolinae
Continuous tree-like scales
James Cummings (2010)
Open Mathematics
Answering a question raised by Luis Pereira, we show that a continuous tree-like scale can exist above a supercompact cardinal. We also show that the existence of a continuous tree-like scale at ℵω is consistent with Martin’s Maximum.
Continuum Problem at Measurable Cardinals
Aleksandar Jovanović (1977)
Zbornik Radova
Correction to: Homological Dimension and Stationary Sets. Math. Z. 180, 1-9 (1982).
Paul C. Eklof (1983)
Mathematische Zeitschrift
Currently displaying 1 – 11 of 11
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