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Universal sets for pointsets properly on the nth level of the projective hierarchy

Published online by Cambridge University Press:  12 March 2014

Greg Hjorth ,
Leigh Humphries  and
Arnold W. Miller
Greg Hjorth
Affiliation:
Department of Mathematics & Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia, URL: www.math.ucla.edu/~greg, E-mail: leighh@unimelb.edu.au
Arnold W. Miller
Affiliation:
University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388, USA, E-mail: miller@math.wisc.edu URL: http://www.math.wisc.edu/~miller
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Abstract

The Axiom of Projective Determinacy implies the existence of a universal set for every n ≥ 1. Assuming there exists a universal set. In ZFC there is a universal set for every α.

Keywords

Universal setsProjective DetermancyWadge reducibilityConstructible UniverseMartin's Axiom
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 237 - 244
Copyright
Copyright © Association for Symbolic Logic 2013

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