I will talk about some results on the Sigma_1(X) and Pi_1(X) definability over H_{kappa^+} of pathological subsets of P(kappa), when there are large cardinals in V_kappa. In particular, if kappa is a limit of measurable cardinals then letting X=H_\kappa\cup OR, there is no Sigma_1(X) wellorder of a subset of P(\kappa) of length \geq\kappa^+, and there is no Sigma_1(X) mad family of cardinality >kappa. However, the existence of regular kappa with large cardinal properties together with Pi_1({kappa}) mad families and maximal independent families are consistent relative to large cardinals. And in M_1, the minimal proper class mouse with a Woodin cardinal, for every uncountable cardinal kappa which is not a limit of measurable cardinals, there is a good Sigma_1(H_kappa\cup {kappa}) wellorder of H_{kappa^+}, where X is as before. Some of the results address questions of Lücke and Müller. Reference: "Low level definability above large cardinals".