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Is Jensen's covering lemma meaningful in a platonist's view?

The typical applications of fine structure theory are finding out the lower bounds of consistency strength of axiom systems. In such a proccess, we also constructs many combinatorial objects in core ...
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Can Jensen's covering lemma be proven easier in generic extensions of L?

Jensen's covering lemma, stating that if there is no $0^\#$ in V, then some covering property holds true, has a very complex proof. In any generic extension L[G] of L, $0^\#$ don't exist, so the ...