Inner models with large cardinal features usually obtained by forcing

Details Inner models with large cardinal features usually obtained by forcing Inner models with large cardinal features usually obtained by forcing

2011-11-03

arxiv.org/abs/1111.0856v1

Mathematics

Logic

Scientific paper

We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible supercompact cardinal. If there is a supercompact cardinal, then there is an inner model with a supercompact cardinal \kappa for which 2^\kappa=\kappa^+, another for which 2^\kappa=\kappa^++ and another in which the least strongly compact cardinal is supercompact. If there is a strongly compact cardinal, then there is an inner model with a strongly compact cardinal, for which the measurable cardinals are bounded below it and another inner model W with a strongly compact cardinal \kappa, such that H_{\kappa^+}^V\subseteq HOD^W. Similar facts hold for supercompact, measurable and strongly Ramsey cardinals. If a cardinal is supercompact up to a weakly iterable cardinal, then there is an inner model of the Proper Forcing Axiom and another inner model with a supercompact cardinal in which GCH+V=HOD holds. Under the same hypothesis, there is an inner model with level by level equivalence between strong compactness and supercompactness, and indeed, another in which there is level by level inequivalence between strong compactness and supercompactness. If a cardinal is strongly compact up to a weakly iterable cardinal, then there is an inner model in which the least measurable cardinal is strongly compact. If there is a weakly iterable limit \delta of <\delta-supercompact cardinals, then there is an inner model with a proper class of Laver-indestructible supercompact cardinals. We describe three general proof methods, which can be used to prove many similar results.

Affiliated with

Also associated with

No associations

Rating

Inner models with large cardinal features usually obtained by forcing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Inner models with large cardinal features usually obtained by forcing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inner models with large cardinal features usually obtained by forcing will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-702716