Regularity Properties on the Generalized Reals
  We investigate regularity properties derived from tree-like forcing notions in the setting of "generalized descriptive set theory", i.e., descriptive set theory on $\kappa^\kappa$ and $2^\kappa$, for regular uncountable cardinals $\kappa$. 
Sy-David Friedman, Yurii Khomskii, Vadim Kulikov
math.LO