Dear all, Let alpha be an ordinal. Let $alpha be the totally ordered set of ordinals below alpha. "Alpha-dependent choice" is the following statement: for any functor A : $alpha ^ op ---> Set, if A_i is nonempty for all i < alpha, and A_i,j : A_j ---> A_i is surjective for all i <= j < alpha, then the limit of A is nonempty. If alpha has a cofinal omega-sequence (i.e. an omega-sequence of ordinals < alpha whose supremum is alpha), then alpha-dependent choice follows from dependent choice. I would think that, if alpha doesn't have a cofinal omega-sequence, then alpha-dependent choice is false. Is there a known counterexample? E.g. in the case alpha = omega_1 (the least uncountable ordinal). Thanks, Paul -- Paul Blain Levy School of Computer Science, University of Birmingham +44 (0)121 414 4792 http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]