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Archive for Mathematical Logic

, Volume 36, Issue 2, pp 137–155 | Cite as

Large cardinals and projective sets

  • Haim Judah
  • Otmar Spinas

Abstract.

We investigate measure and category in the projective hierarchie in the presence of large cardinals. Assuming a measurable larger than \(n\) Woodin cardinals we construct a model where every \(\Delta ^1_{n+4}\)-set is measurable, but some \(\Delta ^1_{n+4}\)-set does not have Baire property. Moreover, from the same assumption plus a precipitous ideal on \(\omega _1\) we show how a model can be forced where every \(\Sigma ^1_{n+4}-\)set is measurable and has Baire property.

Keywords

Large Cardinal Baire Property Precipitous Ideal 
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 Berlin Heidelberg 1997

Authors and Affiliations

  • Haim Judah
    • 1
  • Otmar Spinas
    • 1
  1. 1.Abraham Fraenkel Group for Mathematical Logic, Bar Ilan University, 52900 Ramat Gan, IsraelIL

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