| Title:
|
Ideal version of Ramsey's theorem (English) |
| Author:
|
Filipów, Rafał |
| Author:
|
Mrożek, Nikodem |
| Author:
|
Recław, Ireneusz |
| Author:
|
Szuca, Piotr |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
289-308 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider various forms of Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey's theorem (these are similar to generalizations shown in [P. Frankl, R. L. Graham, and V. Rödl: Iterated combinatorial density theorems. J. Combin. Theory Ser. A 54 (1990), 95–111]. (English) |
| Keyword:
|
ideal of subsets of natural numbers |
| Keyword:
|
Bolzano-Weierstrass theorem |
| Keyword:
|
Bolzano-Weierstrass property |
| Keyword:
|
ideal convergence |
| Keyword:
|
statistical density |
| Keyword:
|
statistical convergence |
| Keyword:
|
subsequence |
| Keyword:
|
monotone sequence |
| Keyword:
|
Ramsey's theorem |
| MSC:
|
05A17 |
| MSC:
|
05D10 |
| MSC:
|
11B05 |
| MSC:
|
40A35 |
| MSC:
|
54A20 |
| idZBL:
|
Zbl 1249.05378 |
| idMR:
|
MR2905404 |
| DOI:
|
10.1007/s10587-011-0073-3 |
| . |
| Date available:
|
2011-06-06T10:24:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141533 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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