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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2010 | 210 | 3 | 269-283

## Negative universality results for graphs

EN

### Abstrakty

EN
It is shown that in many forcing models there is no universal graph at the successors of regular cardinals. The proof, which is similar to the well-known proof for Cohen forcing, is extended to show that it is consistent to have no universal graph at the successor of a singular cardinal, and in particular at $ℵ_{ω+1}$. Previously, little was known about universality at the successors of singulars. Analogous results show it is consistent not just that there is no single graph which embeds the rest, but that it takes the maximal number ($2^λ$ for graphs of size λ) to embed the rest.

269-283

wydano
2010

### Twórcy

autor
• Kurt Gödel Research Center, for Mathematical Logic, Währinger Straße 25, A-1090 Wien, Austria
autor
• Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, A-1040 Wien, Austria