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We investigate measure and category in the projective hierarchie in the presence of large cardinals. Assuming a measurable larger than
Woodin cardinals we construct a model where every
-set is measurable, but some
-set does not have Baire property....
We prove in ZF+DC, e.g. that: if
is regular but non measurable. This is in contrast with the results on measurability for
due to Apter and Magidor [ApMg].
In this paper we show that the theory of fields together with an integrally closed subring, the theory of formally real fields with a real holomorphy ring and the theory of formally
-adic fields with a
-adic holomorphy ring have no model companions in the language of fields augmented...
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