161 research outputs found
Easton supported Jensen coding and projective measure without projective Baire
We prove that it is consistent relative to a Mahlo cardinal that all sets of
reals definable from countable sequences of ordinals are Lebesgue measurable,
but at the same time, there is a set without the Baire property.
To this end, we introduce a notion of stratified forcing and stratified
extension and prove an iteration theorem for these classes of forcings.
Moreover we introduce a variant of Shelah's amalgamation technique that
preserves stratification. The complexity of the set which provides a
counterexample to the Baire property is optimal.Comment: 142 page
Embeddings into outer models
We explore the possibilities for elementary embeddings , where
and are models of ZFC with the same ordinals, , and
has access to large pieces of . We construct commuting systems of such maps
between countable transitive models that are isomorphic to various canonical
linear and partial orders, including the real line
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