Translator Disclaimer
March 2013 Universal sets for pointsets properly on the nth level of the projective hierarchy
Greg Hjorth, Leigh Humphries, Arnold W. Miller
J. Symbolic Logic 78(1): 237-244 (March 2013). DOI: 10.2178/jsl.7801160

Abstract

The Axiom of Projective Determinacy implies the existence of a universal $\underset{\tilde{}}{{\Pi}^1_n}\setminus\underset{\tilde{}}{{\Delta}^1_n}$ set for every $n \geq 1$. Assuming $\rm{MA}(\aleph_{1})+\aleph_{1}=\aleph_{1}^{\mathbb{L}}$ there exists a universal $\underset{\tilde{}}{{\Pi}^1_1}\setminus\underset{\tilde{}}{{\Delta}^1_1}$ set. In ZFC there is a universal $\underset{\tilde{}}{{\Pi}^0_\alpha}\setminus\underset{\tilde{}}{{\Delta}^0_\alpha}$ set for every $\alpha$.

Citation

Download Citation

Greg Hjorth. Leigh Humphries. Arnold W. Miller. "Universal sets for pointsets properly on the nth level of the projective hierarchy." J. Symbolic Logic 78 (1) 237 - 244, March 2013. https://doi.org/10.2178/jsl.7801160

Information

Published: March 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1268.03065
MathSciNet: MR3087073
Digital Object Identifier: 10.2178/jsl.7801160

Subjects:
Primary: 03E15 03E60

Rights: Copyright © 2013 Association for Symbolic Logic

JOURNAL ARTICLE
8 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.78 • No. 1 • March 2013
Back to Top