منابع مشابه
Diagonal Prikry extensions
It is a well-known phenomenon in set theory that problems in infinite combinatorics involving singular cardinals and their successors tend to be harder than the parallel problems for regular cardinals. Examples include the behaviour of cardinal exponentiation, the extent of the tree property, the extent of stationary reflection, and the existence of non-free almost-free abelian groups. The expl...
متن کاملIntermediate models of Prikry generic extensions
We prove that if V ⊆ V[h] is a generic extension by Prikry forcing then every transitive intermediate model M of ZFC , where V $ M ⊆ V[h] , is again a Prikry generic extension of V . Moreover the family of intermediate models is parametrised by P(ω)/finite. The result is proved by studying V-constructibility degrees of sets in V[h] using parameters in V .
متن کاملOn density of old sets in Prikry type extensions
Every set of ordinals of cardinality κ in a Prikry extension with a measure over κ contains an old set of arbitrary large cardinality below κ, and, actually, it can be split into countably many old sets. What about sets bigger cardinalities? Clearly, any set of ordinals in a forcing extension of a regular cardinality above the cardinality of the forcing used, contains an old set of the same car...
متن کاملMathias-Prikry and Laver-Prikry type forcing
We study the Mathias-Prikry and Laver-Prikry forcings associated with filters on ω. We give a combinatorial characterization of Martin’s number for these forcing notions and present a general scheme for analyzing preservation properties for them. In particular, we give a combinatorial characterization of those filters for which the Mathias-Prikry forcing does not add any dominating reals.
متن کاملDegrees of subsets of the measurable cardinal in Prikry generic extensions
We prove that in a Prikry generic extension for a measure U on κ every subset of the measurable cardinal κ in the Prikry extension is constructibly equivalent, over the ground model, to a subsequence of the Prikry sequence.
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2010
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1286198153