The Generalized Borel Conjecture and Strongly Proper Orders

DOI10.2307/2001276zbMath0693.03031OpenAlexW4238513744MaRDI QIDQ3035273

Paul Corazza

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001276

zbMATH Keywords

proper forcingSacks forcingstrong measure zero setGeneralized Borel Conjectureuniformly continuous maps onto [0,1]

Mathematics Subject Classification ID

Descriptive set theory (03E15) Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Consistency and independence results (03E35) Foundations: limits and generalizations, elementary topology of the line (26A03) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05)

Related Items (12)

Topologies making a given ideal nowhere dense or meager ⋮ Perfectly meager sets and universally null sets ⋮ Continuous and smooth images of sets ⋮ Productively Lindelöf and indestructibly Lindelöf spaces ⋮ On countably perfectly meager and countably perfectly null sets ⋮ Sacks forcing, Laver forcing, and Martin's axiom ⋮ Strongly meager sets can be quite big ⋮ Borel’s conjecture and meager-additive sets ⋮ Strong measure zero in Polish groups ⋮ Borel Conjecture, dual Borel Conjecture, and other variants of the Borel Conjecture ⋮ Strong measure zero and meager-additive sets through the prism of fractal measures ⋮ Functions with distant fibers and uniform continuity

Cites Work

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• \(\gamma\)-sets and other singular sets of real numbers
• Singular sets and Baire order
• Proper forcing
• Classical theory of totally imperfect spaces
• On the consistency of Borel's conjecture
• Mapping a set of reals onto the reals
• Variations on Lusin's Theorem
• Why Solovay real produces Cohen real
• On some properties of Hurewicz, Menger, and Rothberger
• Iterated perfect-set forcing
• Some Properties of Measure and Category
• Spaces without Large Projective Subspaces.
• Sur la non-invariance topologique de la propriété λ'
• Multiple Forcing

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