Pseudo definably connected definable sets (Q2813679)
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scientific article; zbMATH DE number 6598146
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pseudo definably connected definable sets |
scientific article; zbMATH DE number 6598146 |
Statements
Pseudo definably connected definable sets (English)
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24 June 2016
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weak o-minimality
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pseudo-definable connectedness
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weak definable connectedness
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strong cell
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0.8680156
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0.8666743
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0.86372405
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0.86043376
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The paper concerns the notion of weak o-minimality introduced by \textit{M. A. Dickmann} [J. Symb. Log. 52, 116--128 (1987; Zbl 0624.03025)] and originally deeply studied by \textit{D. Macpherson} et al. [Trans. Am. Math. Soc. 352, No. 12, 5435--5483 (2000; Zbl 0982.03021)]. The authors introduce the notion of pseudo-definable connectedness in weakly o-minimal structures with strong cell decomposition and prove that every strong cell in these structures is pseudo-definably connected. In addition, they compare the new notion with the notion of weak definable connectedness and show that the pseudo-definable connectedness is stronger.
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