A version of the Erdös-Rado theorem on partitions of the unordered ntuples from uncountable sets is proved, without using the axiom of choice. The case with exponent 1 is just the Sierpinski-Hartogs’ result that א(α) ≤ 2 2α . The liberal use made by Erdös and Rado in [2] of the cardinal arithmetic versions of the axiom of choice enables them to give their result a particularly simple expression...

Recent measurements of inclusive and exclusive semileptonic b branching ratios are reviewed. Model-independent analyses from ARGUS and CLEO connrm the value B(b ! ``X) = 10:4%, while new analyses from ALEPH obtain higher values above 11%. The diierence is not consistent with measured values of b hadron lifetime. New measurements of B(B ! D ? ``) from CLEO and ALEPH are in good agreement. First ...

This is to present work on modifying the Aleph ILP system so that it evaluates the hypothesised clauses in parallel by distributing the data-set among the nodes of a parallel or distributed machine. The paper briefly discusses the MPI specification and the extension of Yap Prolog with an interface to MPI libraries. It then proceeds to describe an implementation of data-parallel clause evaluatio...