Some Applications of Supercompact Extender Based Forcings to Hod
نویسنده
چکیده
Supercompact extender based forcings are used to construct models with HOD cardinal structure different from those of V . In particular, a model with all regular uncountable cardinals measurable in HOD is constructed.
منابع مشابه
Hod-supercompactness, Indestructibility, and Level by Level Equivalence
In an attempt to extend the property of being supercompact but not hod-supercompact to a proper class of indestructibly supercompact cardinals, a theorem is discovered about a proper class of indestructibly supercompact cardinals which reveals a surprising incompatibility. However, it is still possible to force to get a model in which the property of being supercompact but not hod-supercompact ...
متن کاملSupercompact extender based Prikry forcing
The extender based Prikry forcing notion is being generalized to supercompact extenders.
متن کاملHybrid Prikry Forcing
We present a new forcing notion combining diagonal supercompact Prikry focing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ and GCH holds below κ. Moreover we define a scale at κ, which has a stationary set of bad points in the ground model.
متن کاملCoding into HOD via normal measures with some applications
We develop a new method for coding sets while preserving gch in the presence of large cardinals, particularly supercompact cardinals. We will use the number of normal measures carried by a measurable cardinal as an oracle, and therefore, in order to code a subset A of κ, we require that our model contain κ many measurable cardinals above κ. Additionally we will describe some of the applications...
متن کاملSubcomplete Forcing and L-Forcing
ABSRACT In his book Proper Forcing (1982) Shelah introduced three classes of forcings (complete, proper, and semi-proper) and proved a strong iteration theorem for each of them: The first two are closed under countable support iterations. The latter is closed under revised countable support iterations subject to certain standard restraints. These theorems have been heavily used in modern set th...
متن کامل