The Necessary Maximality Principle for c. c. c. forcing is equiconsistent with a weakly compact cardinal

Abstract

The Necessary Maximality Principle for c.c.c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal. The Necessary Maximality Principle for c.c.c. forcing, denoted 2mpccc(R), 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… (More)
DOI: 10.1002/malq.200410045

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Cite this paper

@article{Hamkins2005TheNM, 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={Math. Log. Q.}, year={2005}, volume={51}, pages={493-498} }