Unordered Canonical Ramsey Numbers

We define a weak form of canonical colouring, based on that of P. Erdős and R. Rado (1950, J. London Math. Soc.25, 249–255). This yields a class of unordered canonical Ramsey numbers CR(s, t), again related to the canonical Ramsey numbers ER(2; s) of Erdős and Rado. We present upper and lower bounds (the latter via a construction) for CR(s, t) which are significantly tighter than the best-known corresponding bounds for ER(2; s).