# Sh:370

- Shelah, S., & Soukup, L. (1994).
*On the number of nonisomorphic subgraphs*. Israel J. Math.,**86**(1-3), 349–371. arXiv: math/9401210 DOI: 10.1007/BF02773686 MR: 1276143 -
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}, doi = {10.1007/BF02773686}, mrclass = {03E35 (03E75 05C30)}, mrnumber = {1276143}, mrreviewer = {James Baumgartner}, doi = {10.1007/BF02773686}, note = {\href{https://arxiv.org/abs/math/9401210}{arXiv: math/9401210}}, arxiv_number = {math/9401210} }