English

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

R2 v1 2026-07-22T17:03:16.619Z