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Large cardinals and projective sets

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Large cardinals and projective sets

Archive for Mathematical Logic , Volume 36 (2) – Feb 1, 1997

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 1997 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s001530050059
Publisher site
See Article on Publisher Site

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.

Journal

Archive for Mathematical LogicSpringer Journals

Published: Feb 1, 1997

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