On the number of non-isomorphic subgraphs

S. Shelah; L. Soukup

doi:10.1007/BF02773686

On the number of non-isomorphic subgraphs

S. Shelah^*
, L. Soukup

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let {Mathematical expression} be the family of graphs on ω₁ without cliques or independent subsets of size w₁. We prove that (a) it is consistent with CH that every Gε {Mathematical expression} has 2^ω many pairwise non-isomorphic subgraphs, (b) the following proposition holds in L: (*)there is a Gε {Mathematical expression} such that for each partition (A, B) of ω₁ either G≅G[A] or G≅G[B], (c) the failure of (*) is consistent with ZFC.

Original language	English
Pages (from-to)	349-371
Number of pages	23
Journal	Israel Journal of Mathematics
Volume	86
Issue number	1-3
DOIs	https://doi.org/10.1007/BF02773686
State	Published - Oct 1994

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On the number of non-isomorphic subgraphs

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