Antichains in the powerset of \(\mathbb{R}\): Realisation through induction (Q2732522)
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scientific article; zbMATH DE number 1623796
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Antichains in the powerset of \(\mathbb{R}\): Realisation through induction |
scientific article; zbMATH DE number 1623796 |
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25 February 2002
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Bernstein set
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incomparable sets
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antichain
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transfinite induction
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Antichains in the powerset of \(\mathbb{R}\): Realisation through induction (English)
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It is well known that there exists a family of \(c^+\) Bernstein sets in \textbf{R} which are pairwise incomparable under homeomorphic embeddability. Here the authors present a new proof of this fact, via transfinite induction, and show how this technique can be used to solve similar problems concerning ``the possible order types of families of substructures of a given structure''.
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0.7433223128318787
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