On maximum conservative extensions
Henry Towsner · Computability · 2015
We investigate the set of Π 1 2 sentences which are Π 1 1 conservative over theories of second order arithmetic. We exhibit new elements of these sets and conclude that the sets are Π 2 complete. Along the way, we show that, over the theory RCA 0 , induction for Σ n formulas has essentially no consequences for Δ n+1 formulas.