The Necessary Maximality Principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal
Logic
2007-05-23 v1
Abstract
The Necessary Maximality Principle for c.c.c. forcing asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already true in the minimal extension containing the real. We show that this principle is equiconsistent with the existence of a weakly compact cardinal.
Keywords
Cite
@article{arxiv.math/0403165,
title = {The Necessary Maximality Principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal},
author = {Joel David Hamkins and W. Hugh Woodin},
journal= {arXiv preprint arXiv:math/0403165},
year = {2007}
}
Comments
11 pages