A large Pi-1-2 set absolute for set forcing
逻辑
2009-09-25 v1
摘要
Let k be a definable L-cardinal. Then there is a set of reals X, class-generic over L, such that L(X) and L have the same cardinals, X has size k in L(X) and some pi-1-2 formula defines X in all set-generic extensions of L(X). Two corollaries, both assuming the consistency of an inaccessible: It is consistent for the Perfect Set Property to hold for boldface sigma-1-2 sets, yet fail for some lightface pi-1-2 set. It is consistent that the Perfect Set Property holds for boldface sigma-1-2 sets yet some lightface pi-1-2 wellordering of some set of reals has length aleph-1000.
引用
@article{arxiv.math/9212202,
title = {A large Pi-1-2 set absolute for set forcing},
author = {Sy D. Friedman},
journal= {arXiv preprint arXiv:math/9212202},
year = {2009}
}