Article
| Title: | Coloring triangles and rectangles (English) |
| Author: | Zapletal, Jindřich |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 83-96 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | It is consistent that ZF + DC holds, the hypergraph of rectangles on a given Euclidean space has countable chromatic number, while the hypergraph of equilateral triangles on $\mathbb{R}^2$ does not. (English) |
| Keyword: | real algebraic geometry |
| Keyword: | algebraic hypergraph |
| Keyword: | chromatic number |
| Keyword: | geometric set theory |
| Keyword: | consistency result |
| MSC: | 03E35 |
| MSC: | 05C15 |
| MSC: | 14P99 |
| idZBL: | Zbl 07790584 |
| idMR: | MR4631792 |
| DOI: | 10.14712/1213-7243.2023.020 |
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| Date available: | 2023-08-28T09:47:05Z |
| Last updated: | 2024-02-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151803 |
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| Reference: | [2] Erdös P., Kakutani S.: On non-denumerable graphs.Bull. Amer. Math. Soc. 49 (1943), 457–461. MR 0008136, 10.1090/S0002-9904-1943-07954-2 |
| Reference: | [3] Erdös P., Komjáth P.: Countable decompositions of $\mathbb{R}^2$ and $\mathbb{R}^3$.Discrete Comput. Geom. 5 (1990), no. 4, 325–331. MR 1043714 |
| Reference: | [4] Ihoda J. I., Shelah S.: Souslin forcing.J. Symbolic Logic 53 (1998), no. 4, 1188–1207. MR 0973109, 10.2307/2274613 |
| Reference: | [5] Jech T.: Set Theory.Springer Monographs in Mathematics, Springer, Berlin, 2003. Zbl 1007.03002, MR 1940513 |
| Reference: | [6] Larson P., Zapletal J.: Geometric Set Theory.Mathematical Surveys and Monographs, 248, American Mathematical Society, Providence, 2020. MR 4249448, 10.1090/surv/248 |
| Reference: | [7] Marker D.: Model Theory: An Introduction.Graduate Texts in Mathematics, 217, Springer, New York, 2002. MR 1924282 |
| Reference: | [8] Schmerl J. H.: Avoidable algebraic subsets of Euclidean space.Trans. Amer. Math. Soc. 352 (2000), no. 6, 2479–2489. MR 1608502, 10.1090/S0002-9947-99-02331-4 |
| Reference: | [9] Zapletal J.: Noetherian spaces in choiceless set theory.available at arXiv:2101.03434v3 [math.LO] (2022), 23 pages. |
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