On the number of non-isomorphic subgraphs (Q1327515)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of non-isomorphic subgraphs |
scientific article |
Statements
On the number of non-isomorphic subgraphs (English)
0 references
19 June 1994
0 references
It is consistent with CH that every graph on \(\omega_ 1\) with no uncountable clique or independent set has \(2^{\aleph_ 1}\) non- isomorphic subgraphs. It is also consistent that every graph \(G\) as above has a vertex decomposition \(\omega_ 1= A\cup B\) such that neither \(G\upharpoonright A\) nor \(G\upharpoonright B\) is isomorphic to \(G\). \(\text{V}=\text{L}\) implies the negation of this statement.
0 references
Aronszajn trees
0 references
uncountable graphs
0 references
iterated forcing
0 references
uncountable clique
0 references
vertex decomposition
0 references
