# Sh:491

• Gilchrist, M., & Shelah, S. (1996). Identities on cardinals less than \aleph_\omega. J. Symbolic Logic, 61(3), 780–787.
• 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},
mrnumber = {1412509},
mrclass = {03E05 (03E10 03E35)},
doi = {10.2307/2275784},
note = {\href{https://arxiv.org/abs/math/9505215}{arXiv: math/9505215}},
arxiv_number = {math/9505215}
}