特殊篇章玄宇宙计划原文序列部分章 (10-6)

But there are clear rebuttals to this argument. Consider, for instance, Lévy-

Shocnfield absoluteness,the absolutcness of Σ¹₂ statcments with respect to arbitrary outer models. This is provable in ZFC even if one allows arbitrary

real parameters. Extrapolation then naturally leads to Σ¹ʀ.absoluteness with arbitrary real parameters. But even Σ¹₃ absoluteness with arbitrary real

parameters is provably false. With arbitrary real parameters a consistent

principle can only be obtaincd by artificially taking "outer model” to mean

"set-generic outer model". As soon as one relaxes this to class-generic outer

models, the principle becomes inconsistent.

So, if one is so easily led to inconsistency when extrapolating from Σ¹₂ to Σ¹₃ absoluteness, how can one justify the extrapolation from Σ¹₁ measurability to projcctivemeasurability?

More reasonable would be the extrapolation with out parameters. Indeed,paramcter-free Σ¹₃ absoluteness, unlike the version

with arbitrary real parameters, is consistent with (and indeed follows from)the IMH.Thus a natural conclusion with regard to projective statements is the following: The principle of uniformity, which asserts that properties that hold for parameter-free projcctive sets also hold for arbitrary projective sets

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