The full basis theorem does not imply analytic wellordering

A finite support product of ${\omega }_1$ clones of Jensen's minimal ${\Pi }_2^1$ 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.     

Computation of the Ordinal of Braids

There exists a linear ordering on braids coming from left distributivity assumptions. The restriction of this order to positive braids is a wellordering. We present here some tools and an effective algorithm for the computation of the rank of any positive braid in this wellordering.     

二型序数与良序二型类的同构

证明了二型序数具有如下性质对任一二型类良序结构［A,R］,存在惟一的二型序数B,使得［B,E］与［A,R］同构,特别地对良序聚会［