Relations between notions of gaplessness for non-Archimedean fields
| Authors |
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| Publication date | 2020 |
| Journal | Houston Journal of Mathematics |
| Volume | Issue number | 46 | 4 |
| Pages (from-to) | 1017-1031 |
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| Abstract | In this paper, we are studying the relationship between notions of gaplessness for non-Archimedean ordered fields, in particular three generalised Bolzano-Weierstraß properties: the Sikorski property (which fails for saturated fields), the Keisler-Schmerl property, and the weak Bolzano-Weierstraß property introduced by Carl, Galeotti, and Löwe. We show that the weak Bolzano-Weierstraß property is “Bolzano-Weierstraß minus Cauchy completeness” and is equivalent the tree property of the base number of the field. We furthermore improve on a number of results by Carl, Galeotti, and Löwe. |
| Document type | Article |
| Language | English |
| Other links | https://www.math.uh.edu/~hjm/Vol46-4.html |
| Downloads |
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