A conservative extension of first-order logic and its application to theorem proving

We define a weak second--order extension of first--order logic. We prove a second--order cut elimination theorem for this logic and use this to prove a conservativity and a realisability result. We give applications to formal program development and theorem proving, in particular, in modeling techniques in formal metatheory

Recent Experiments with Bose-Condensed Gases at JILA

We consider a binary mixture of two overlapping Bose-Einstein condensates in two different hyperfine states of \Rb87 with nearly identical magnetic moments. Such a system has been simply realized through application of radiofrequency and microwave radiation which drives a two-photon transition between the two states. The nearly identical magnetic moments afford a high degree of spatial overlap, permitting a variety of new experiments. We discuss some of the conditions under which the magnetic moments are identical, with particular emphasis placed on the requirements for a time-averaged orbiting potential (TOP) magnetic trap.Comment: 9 pages, 5 figures; corrected post-publication editio