Sh:370

• Shelah, S., & Soukup, L. (1994). On the number of nonisomorphic subgraphs. Israel J. Math., 86(1-3), 349–371.
• Abstract:
Let \mathcal 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{\mathcal K} has 2^{\omega_1} many pairwise non-isomorphic subgraphs,

2) the following proposition holds in L: (*) there is a G\in{\mathcal 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.

• published version (23p)
Bib entry
@article{Sh:370,
author = {Shelah, Saharon and Soukup, Lajos},
title = {{On the number of nonisomorphic subgraphs}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {86},
number = {1-3},
year = {1994},
pages = {349--371},
issn = {0021-2172},
mrnumber = {1276143},
mrclass = {03E35 (03E75 05C30)},
doi = {10.1007/BF02773686},
note = {\href{https://arxiv.org/abs/math/9401210}{arXiv: math/9401210}},
arxiv_number = {math/9401210}
}