Journal article
The subseries number
- Abstract:
- Every conditionally convergent series of real numbers has a divergent subseries. How many subsets of the natural numbers are needed so that every conditionally convergent series diverges on the subseries corresponding to one of these sets? The answer to this question is defined to be the subseries number, a new cardinal characteristic of the continuum. This cardinal is bounded below by N1 and above by the cardinality of the continuum, but it is not provably equal to either. We define three natural variants of the subseries number, and compare them with each other, with their corresponding rearrangement numbers, and with several well-studied cardinal characteristics of the continuum. Many consistency results are obtained from these comparisons, and we obtain another by computing the value of the subseries number in the Laver model.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 363.0KB, Terms of use)
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- Publisher copy:
- 10.4064/fm667-11-2018
Authors
- Publisher:
- Polskiej Akademii Nauk, Instytut Matematyczny
- Journal:
- Fundamenta Mathematicae More from this journal
- Volume:
- 247
- Pages:
- 49-85
- Publication date:
- 2019-03-15
- DOI:
- EISSN:
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1730-6329
- ISSN:
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0016-2736
- Keywords:
- Pubs id:
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pubs:1039439
- UUID:
-
uuid:24fce7b3-9592-4fa5-97c0-5745c162eacb
- Local pid:
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pubs:1039439
- Source identifiers:
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1039439
- Deposit date:
-
2019-12-17
Terms of use
- Copyright holder:
- Instytut Matematyczny PAN
- Copyright date:
- 2019
- Notes:
- © Instytut Matematyczny PAN, 2019. This is the accepted manuscript version of the article. The final version is available online from the Polish Academy of Sciences, Institute of Mathematics at: 10.4064/fm667-11-2018
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