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SMALL UNIVERSAL FAMILIES OF GRAPHS ON ℵω + 1

Published online by Cambridge University Press:  29 June 2016

JAMES CUMMINGS ,
MIRNA DŽAMONJA  and
CHARLES MORGAN
JAMES CUMMINGS
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCESCARNEGIE MELLON UNIVERSITYPITTSBURGH PA15213-3890, USAE-mail:[email protected]
MIRNA DŽAMONJA
Affiliation:
SCHOOL OF MATHEMATICSUNIVERSITY OF EAST ANGLIA NORWICH, NR4 7TJ, UKE-mail:[email protected]
CHARLES MORGAN
Affiliation:
DEPARTMENT OF MATHEMATICSUNIVERSITY COLLEGE LONDONGOWER STREET, LONDON WC1E 6BT, UKE-mail:[email protected]
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Abstract

We prove that it is consistent that $\aleph _\omega $ is strong limit, $2^{\aleph _\omega } $ is large and the universality number for graphs on $\aleph _{\omega + 1} $ is small. The proof uses Prikry forcing with interleaved collapsing.

Keywords

UniversalitygraphsPrikry forcingiterated forcingmaster conditionssuccessors of singular cardinalsLaver indestructibility
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016 , pp. 541 - 569
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

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