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.     

Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

Nano palladium supported on high‐surface‐area metal–organic framework MIL‐101: an efficient catalyst for Sonogashira coupling of aryl and heteroaryl bromides with alkynes

Palladium nanoparticle‐incorporated metal–organic framework MIL‐101 (Pd/MIL‐101) was successfully synthesized and characterized using X‐ray diffraction, nitrogen physisorption, X‐ray photoelectron, UV–visible and infrared spectroscopies, and transmission electron microscopy. The characterization techniques confirmed high porosity and high surface area of MIL‐101 and high stability of nano‐size palladium particles. Pd/MIL‐101 nanocomposite was investigated for the Sonogashira cross‐coupling reaction of aryl and heteroaryl bromides with various alkynes under copper‐free conditions. The reusability of the catalyst was tested for up to four cycles without any significant loss in catalytic activity. Copyright © 2015 John Wiley & Sons, Ltd.