On Maximum Conservative Extensions
Abstract
We investigate the set of Pi-1-2 sentences which are Pi-1-1 conservative over the theories of reverse mathematics RCA0+ISigman and ACA0. We exhibit new elements of these sets and conclude that the sets are Pi2 complete. Along the way, we show that, over the theory RCA, induction for Sigma-n formulas has essentially no consequences for Delta-(n+1) formulas.
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