read all of Enderton
typeset and read and understand my Feferman notes
read and understand all Pratt's course notes (universal algebra, category theory, chu spaces)
proof theory
http://en.wikipedia.org/wiki/Intermediate_logic
"Classical logic is the only coatom in the lattice of superintuitionistic logics; the lattice of intermediate logics also has a unique coatom, namely SmL?."
"Smetanich's logic (SmL?): IPC + (¬q → p) → (((p → q) → p) → p)" note: (((p → q) → p) → p) is Pierce's law
curry-howard isomorphism
http://en.wikipedia.org/wiki/Realizability
http://en.wikipedia.org/wiki/Heyting_arithmetic
http://en.wikipedia.org/wiki/Markov%27s_principle
curry-howard isomorphism
http://en.wikipedia.org/wiki/Lambda_cube