Two dichotomy theorems on colourability of non-analytic graphs
Fundamenta Mathematicae, Tome 154 (1997) no. 2, pp. 183-201
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove: Theorem 1. Let κ be an uncountable cardinal. Every κ-Suslin graph G on reals satisfies one of the following two requirements: (I) G admits a κ-Borel colouring by ordinals below κ; (II) there exists a continuous homomorphism (in some cases an embedding) of a certain locally countable Borel graph $G_0$ into G. Theorem 2. In the Solovay model, every OD graph G on reals satisfies one of the following two requirements: (I) G admits an OD colouring by countable ordinals; (II) as above.
@article{10_4064_fm_154_2_183_201,
author = {Vladimir Kanovei},
title = {Two dichotomy theorems on colourability of non-analytic graphs},
journal = {Fundamenta Mathematicae},
pages = {183--201},
publisher = {mathdoc},
volume = {154},
number = {2},
year = {1997},
doi = {10.4064/fm-154-2-183-201},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-154-2-183-201/}
}
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Vladimir Kanovei. Two dichotomy theorems on colourability of non-analytic graphs. Fundamenta Mathematicae, Tome 154 (1997) no. 2, pp. 183-201. doi: 10.4064/fm-154-2-183-201
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