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SMALL UNIVERSAL FAMILIES OF GRAPHS ON ℵ ω + 1

Published online by Cambridge University Press:  29 June 2016

JAMES CUMMINGS
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES CARNEGIE MELLON UNIVERSITY PITTSBURGH PA 15213-3890, USA E-mail: jcumming@andrew.cmu.edu
MIRNA DŽAMONJA
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF EAST ANGLIA NORWICH, NR4 7TJ, UK E-mail: m.dzamonja@uea.ac.uk
CHARLES MORGAN
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY COLLEGE LONDON GOWER STREET, LONDON WC1E 6BT, UK E-mail: charles.morgan@ucl.ac.uk

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.

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Articles
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

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