I came across some old notes that seem to be dubious, with no references. So please correct:(adsbygoogle = window.adsbygoogle || []).push({});

The notes say that if Ramsey cardinals exist, and the constructible universe L is regarded as a set, and P_{Def}(.) is taking the constructible power set (i.e., subsets are formed using Def), then

(V_{Ramsey card},∈) |= P_{Def}(L) is countable & P_{Def}(P_{Def}(L)) is uncountable.

Thanks for corrections or comments.

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# I If Ramsey cardinals exist, all powers using Def are countable?

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