A good lightface Δn1 well-ordering of the reals does not imply the existence of boldface Δn−11 well-orderings

Vladimir Kanovei,Vassily Lyubetsky

Annals of Pure and Applied Logic(2024)

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摘要
We make use of a finite support product of the Jensen-type forcing notions to define a model of the set theory ZFC in which, for a given n≥3, there exists a good lightface Δn1 well-ordering of the reals but there are no any (not necessarily good) well-orderings in the boldface class Δn−11.
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关键词
projective classes,well-orderings,Jensen's forcing
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