Coloring triangles and rectangles

Jindřich Zapletal

Commentationes Mathematicae Universitatis Carolinae (2023)

  • Volume: 64, Issue: 1, page 83-96
  • ISSN: 0010-2628

Abstract

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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 does not.

How to cite

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Zapletal, Jindřich. "Coloring triangles and rectangles." Commentationes Mathematicae Universitatis Carolinae 64.1 (2023): 83-96. <http://eudml.org/doc/299364>.

@article{Zapletal2023,
abstract = {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.},
author = {Zapletal, Jindřich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {real algebraic geometry; algebraic hypergraph; chromatic number; geometric set theory; consistency result},
language = {eng},
number = {1},
pages = {83-96},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Coloring triangles and rectangles},
url = {http://eudml.org/doc/299364},
volume = {64},
year = {2023},
}

TY - JOUR
AU - Zapletal, Jindřich
TI - Coloring triangles and rectangles
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 1
SP - 83
EP - 96
AB - 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.
LA - eng
KW - real algebraic geometry; algebraic hypergraph; chromatic number; geometric set theory; consistency result
UR - http://eudml.org/doc/299364
ER -

References

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  3. Erdös P., Komjáth P., Countable decompositions of and , Discrete Comput. Geom. 5 (1990), no. 4, 325–331. MR1043714
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  5. Jech T., Set Theory, Springer Monographs in Mathematics, Springer, Berlin, 2003. Zbl1007.03002MR1940513
  6. Larson P., Zapletal J., 10.1090/surv/248, Mathematical Surveys and Monographs, 248, American Mathematical Society, Providence, 2020. MR4249448DOI10.1090/surv/248
  7. Marker D., Model Theory: An Introduction, Graduate Texts in Mathematics, 217, Springer, New York, 2002. MR1924282
  8. Schmerl J. H., 10.1090/S0002-9947-99-02331-4, Trans. Amer. Math. Soc. 352 (2000), no. 6, 2479–2489. MR1608502DOI10.1090/S0002-9947-99-02331-4
  9. Zapletal J., Noetherian spaces in choiceless set theory, available at arXiv:2101.03434v3 [math.LO] (2022), 23 pages. 

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