### On the number of non-isomorphic subgraphs

by Shelah and Soukup. [ShSo:370]

Israel J Math, 1994

Let K be the family of graphs on omega_1
without cliques or independent subsets of size omega_1 .
We prove that:
1) it is consistent with CH that every G in K has
2^{omega_1} many pairwise non-isomorphic subgraphs,
2) the following proposition holds in L:
(*) there is a G in K such that for each partition
(A,B) of omega_1 either G cong G[A] or G cong G[B],
3) the failure of (*) is consistent with ZFC.

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