Generalizations of the Weak Law of the Excluded Middle
  We study a class of formulas generalizing the weak law of the excluded middle, and provide a characterization of these formulas in terms of Kripke frames and Brouwer algebras. We use these formulas to separate logics corresponding to factors of the Medvedev lattice. 
Andrea Sorbi and Sebastiaan A. Terwijn
math.LO