Preserving P - points in definable forcing II ∗
نویسنده
چکیده
I will prove iteration and product preservation theorems related to Ppoint preservation based on the first part of the paper. I will also provide counterexamples to possible strengthenings of the presented results.
منابع مشابه
Preserving P-points in definable forcing∗
I isolate a simple condition that is equivalent to preservation of Ppoints in definable proper forcing.
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We show that there is a class-sized partial order P with the property that forcing with P preserves ZFC, supercompact cardinals, inaccessible cardinals and the value of 2κ for every inaccessible cardinal κ and, if κ is an inaccessible cardinal and A is an arbitrary subset of κκ, then there is a P-generic extension of the ground model V in which A is definable in 〈H(κ+)V[G],∈〉 by a Σ1-formula wi...
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I prove forcing preservation theorems for products of definable partial orders preserving cofinality of the meager or null ideal. Rectangular Ramsey theorems for the related ideals follow from the proofs.
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This paper deals with the question whether the assumption that for every inaccessible cardinal κ there is a well-order of H(κ+) definable over the structure 〈H(κ+),∈〉 by a formula without parameters is consistent with the existence of (large) large cardinals and failures of the GCH. We work under the assumption that the SCH holds at every singular fixed point of the i-function and construct a c...
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تاریخ انتشار 2008