A note on Hindman-type theorems for uncountable cardinals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866915335511212032 |
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| author | Carlucci, Lorenzo |
| author_facet | Carlucci, Lorenzo |
| contents | Recent results of Hindman, Leader and Strauss and of Fernández-Bretón and Rinot showed that natural versions of Hindman's Theorem fail {\em for all} uncontable cardinals. On the other hand, Komjáth proved a result in the positive direction, showing that {\em there are} arbitrarily large abelian groups satisfying {\em some} Hindman-type property. In this note we show how a family of natural Hindman-type theorems for uncountable cardinals can be obtained by adapting some recent results of the author from their original countable setting. We also show how lower bounds for {\em some} of the variants considered can be obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_06706 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A note on Hindman-type theorems for uncountable cardinals Carlucci, Lorenzo Combinatorics Logic 03E02 (Primary), 05A18, 03E75, 05D10, 20M14 (Secondary) Recent results of Hindman, Leader and Strauss and of Fernández-Bretón and Rinot showed that natural versions of Hindman's Theorem fail {\em for all} uncontable cardinals. On the other hand, Komjáth proved a result in the positive direction, showing that {\em there are} arbitrarily large abelian groups satisfying {\em some} Hindman-type property. In this note we show how a family of natural Hindman-type theorems for uncountable cardinals can be obtained by adapting some recent results of the author from their original countable setting. We also show how lower bounds for {\em some} of the variants considered can be obtained. |
| title | A note on Hindman-type theorems for uncountable cardinals |
| topic | Combinatorics Logic 03E02 (Primary), 05A18, 03E75, 05D10, 20M14 (Secondary) |
| url | https://arxiv.org/abs/1703.06706 |