On the number of non-isomorphic subgraphs

Details On the number of non-isomorphic subgraphs On the number of non-isomorphic subgraphs

1994-01-15

arxiv.org/abs/math/9401210v1

Israel J. Math. 86 (1994), 349--371

Mathematics

Logic

Scientific paper

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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