Negative universality results for graphs

• Autorzy: S.-D. Friedman , K. Thompson
• Języki publikacji: 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.

Kategorie tematyczne

• 03E55: Large cardinals
• 03E05: Other combinatorial set theory
• 03E75: Applications of set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 210
• Numer: 3
• Strony: 269-283

Daty

wydano

2010

Twórcy

autor

S.-D. Friedman

• Kurt Gödel Research Center, for Mathematical Logic, Währinger Straße 25, A-1090 Wien, Austria

autor

K. Thompson

• Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, A-1040 Wien, Austria

Identyfikatory

DOI

10.4064/fm210-3-3