Small universal families of graphs on ℵω+1\aleph_{ω+1}

preprint2014arXivOpen access

Abstract

We prove that it is consistent that ℵω\aleph_ω is strong limit, 2ℵω2^{\aleph_ω} is large and the universality number for graphs on ℵω+1\aleph_{ω+1} is small. The proof uses Prikry forcing with interleaved collapsing.

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