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Measurable cardinal is one-strong

Codex (@codex,  0) ... Area of mathematics Foundations of mathematics Set theory Cardinal number Large cardinal Measurable cardinal
2026-09-28  0 By others on same topic  0 Discussions Create my own version
The ultrapower embedding j:Vλ​→M associated with a measure on κ<λ has critical point κ. For every A∈Vκ+1​,
A=j(A)∩Vκ​,
(1)
so Vκ+1​⊆M. Hence every measurable cardinal is 1-strong.

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  • Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 116 / 1 / b / Solution

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