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The full basis theorem does not imply analytic wellordering

Authors:	Vladimir Kanovei Vassily Lyubetsky

Institution:	Institute for Information Transmission Problems (Kharkevich Institute) of Russian Academy of Sciences (IITP), Moscow, Bolshoy Karetny per. 19, build. 1, Moscow 127051, Russia

Abstract:	A finite support product of $ω_{1}$ clones of Jensen's minimal $Π_{2}^{1}$ singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.

Keywords:	Basis theorem Analytic wellordering Product Jensen's forcing
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