A countable definable set containing no definable elements
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Publication:679849
DOI10.1134/S0001434617090048zbMath1420.03130arXiv1408.3901OpenAlexW3106300234MaRDI QIDQ679849
Vassily Lyubetsky, Kanovei, Vladimir
Publication date: 22 January 2018
Published in: Mathematical Notes (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1408.3901
Descriptive set theory (03E15) Consistency and independence results (03E35) Other notions of set-theoretic definability (03E47)
Related Items (17)
On Russell typicality in set theory ⋮ Models of set theory in which the separation theorem fails ⋮ Definable \(\mathsf{E}_0\) classes at arbitrary projective levels ⋮ Typicality à la Russell in set theory ⋮ Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes ⋮ The full basis theorem does not imply analytic wellordering ⋮ A Groszek‐Laver pair of undistinguishable ‐classes ⋮ A good lightface \(\varDelta_n^1\) well-ordering of the reals does not imply the existence of boldface \(\mathbf{\Delta}_{n - 1}^1\) well-orderings ⋮ A classical way forward for the regularity and normalization problems ⋮ Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy ⋮ A definable \(E_0\) class containing no definable elements ⋮ Countable OD sets of reals belong to the ground model ⋮ Borel OD sets of reals are OD-Borel in some simple models ⋮ Definable Hamel bases and ${\sf AC}_\omega ({\mathbb R})$ ⋮ An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited ⋮ A model of second-order arithmetic satisfying AC but not DC ⋮ Definable elements of definable Borel sets
Cites Work
- An effective minimal encoding of uncountable sets
- Counterexamples to countable-section \(\varPi_2^1\) uniformization and \(\varPi_3^1\) separation
- A cofinal family of equivalence relations and Borel ideals generating them
- A model of set-theory in which every set of reals is Lebesgue measurable
- On coding uncountable sets by reals
- Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes
- On the Leibniz–Mycielski axiom in set theory
- A Groszek‐Laver pair of undistinguishable ‐classes
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