The Baire category theorem and cardinals of countable cofinality

DOI10.2307/2273142zbMath0487.03026OpenAlexW2044269524MaRDI QIDQ3947655

Arnold W. Miller

Publication date: 1982

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2273142

zbMATH Keywords

meager setsBaire categoryreal linecountable cofinalityideal of measure zero sets

Mathematics Subject Classification ID

Consistency and independence results (03E35) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Consistency and independence results in general topology (54A35) Measures and integrals in product spaces (28A35)

Related Items (13)

Cardinal invariants of the continuum and combinatorics on uncountable cardinals ⋮ A Characterization of the Least Cardinal for which the Baire Category Theorem Fails ⋮ Baire numbers, uncountable Cohen sets and perfect-set forcing ⋮ A generalization of the open mapping theorem and a possible generalization of the Baire category theorem ⋮ Some Properties of Measure and Category ⋮ Adding Dominating Reals with the Random Algebra ⋮ Properties of ideals on the generalized Cantor spaces ⋮ On the Covering and the Additivity Number of the Real Line ⋮ Set theoretic properties of Loeb measure ⋮ Game ideals ⋮ Finite combinations of Baire numbers ⋮ On the cofinality of the smallest covering of the real line by meager sets ⋮ Co-absolutes of \(U(\omega_ 1)\)

Cites Work

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• An Infinite-Dimensional Compactum with no Positive-Dimensional Compact Subsets-A Simpler Construction
• Internal cohen extensions
• Spaces homeomorphic to $\left( {2^\alpha } \right)_\alpha$
• Independence results concerning the number of nowhere dense sets necessary to cover the real line
• Products of Separable Spaces

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