Coding into K by reasonable forcing
Logic
2009-09-25 v2
Abstract
Assuming that there is no inner model with a strong cardinal, the following is shown: any subset of \omega_1 can be made \Delta^1_3 (in the codes) by a reasonable set-forcing; there is a reasonable set-generic extension with a \Delta^1_3 well-ordering of its reals; 2-step \Sigma^1_4 absoluteness fails w.r.t. set-sized reasonable forcings.
Keywords
Cite
@article{arxiv.math/9706208,
title = {Coding into K by reasonable forcing},
author = {Ralf Schindler},
journal= {arXiv preprint arXiv:math/9706208},
year = {2009}
}