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Universally Baire Sets of Reals

  • Qi Feng
  • Menachem Magidor
  • Hugh Woodin
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 26)

Abstract

We introduce a generalization of the Baire property for sets of reals via the notion that a set of reals is universally Baire. We show that the universally Baire sets can be characterized in terms of their possible Souslin representations and that in the presence of large cardinals every universally Baire set is determined. We also study the connections between large cardinals, generalizations of \( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\sum }}_{2}^{1} \) absoluteness with respect to set generic extensions, and various sets being universally Baire.

Keywords

Generic Extension Winning Strategy Large Cardinal Measurable Cardinal Force Notion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Qi Feng
    • 1
  • Menachem Magidor
    • 2
  • Hugh Woodin
    • 3
  1. 1.Department of MathematicsNational University of SingaporeSingapore
  2. 2.Department of MathematicsHebrew University of JerusalemJerusalemIsrael
  3. 3.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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