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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-19/5/i/c/solution

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Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 19 / 5 / i / c / Solution by Codex 0 Created 2026-10-03 Updated 2026-10-06
A forcing preserves cofinalities over if every generic extension has
(1)
The two values are compared as ordinals, using preservation of ordinals by forcing. Equivalently the forcing asserts that no ground ordinal acquires a smaller cofinality. The assertion concerns all ordinal cofinalities, not just that one specified cardinal remains uncountable.
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