# Sh:491

- Gilchrist, M., & Shelah, S. (1996).
*Identities on cardinals less than \aleph_\omega*. J. Symbolic Logic,**61**(3), 780–787. arXiv: math/9505215 DOI: 10.2307/2275784 MR: 1412509 -
Abstract:

Let \kappa be an uncountable cardinal and the edges of a complete graph with \kappa vertices be colored with \aleph_0 colors. For \kappa>2^{\aleph_0} the Erdős-Rado theorem implies that there is an infinite monochromatic subgraph. However, if \kappa\leq 2^{\aleph_0}, then it may be impossible to find a monochromatic triangle. This paper is concerned with the latter situation. We consider the types of colorings of finite subgraphs that must occur when \kappa\leq 2^{\aleph_0}. In particular, we are concerned with the case \aleph_1\leq\kappa\leq\aleph_\omega - published version (9p)

Bib entry

@article{Sh:491, author = {Gilchrist, Martin and Shelah, Saharon}, title = {{Identities on cardinals less than $\aleph_\omega$}}, journal = {J. Symbolic Logic}, fjournal = {The Journal of Symbolic Logic}, volume = {61}, number = {3}, year = {1996}, pages = {780--787}, issn = {0022-4812}, doi = {10.2307/2275784}, mrclass = {03E05 (03E10 03E35)}, mrnumber = {1412509}, mrreviewer = {Pierre Matet}, doi = {10.2307/2275784}, note = {\href{https://arxiv.org/abs/math/9505215}{arXiv: math/9505215}}, arxiv_number = {math/9505215} }