The full basis theorem does not imply analytic wellordering

2017/02/12 by Kanovei, Vladimir, Lyubetsky, Vassily · 1 citation
#03E15 #03E35 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1702.03566

Abstract

We make use of a finite support product of ω₁ clones of the Jensen minimal \varPi¹₂ singleton forcing to obtain a model of ZFC in which every non-empty lightface analytically definable set of reals contains a lightface analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the continuum.

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