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

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

2004-03-09

arxiv.org/abs/math/0403165v1

Mathematics

Logic

11 pages

Scientific paper

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.

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