No universal graphs at uncountable regular cardinals
Mohammad Golshani
TL;DR
This paper demonstrates, assuming a strong cardinal, that in a certain model of ZFC, no universal graph exists for any uncountable regular cardinal, highlighting limitations in graph universality at large cardinals.
Contribution
It constructs a model of ZFC with no universal graphs at uncountable regular cardinals, given the assumption of a strong cardinal, advancing understanding of graph universality in set theory.
Findings
No universal graphs at uncountable regular cardinals in the constructed model
Assumption of a strong cardinal is sufficient for this result
The result applies to all uncountable regular cardinals in the model
Abstract
Assuming the existence of a strong cardinal, we find a model of ZFC in which for each uncountable regular cardinal there is no universal graph of size .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras