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Large cardinals and projective sets


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.

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Received October 12, 1994

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Judah, H., Spinas, O. Large cardinals and projective sets . Arch Math Logic 36, 137–155 (1997).

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  • Large Cardinal
  • Baire Property
  • Precipitous Ideal