English

On Maximum Conservative Extensions

Logic 2013-08-26 v2

Abstract

We investigate the set of Pi-1-2 sentences which are Pi-1-1 conservative over the theories of reverse mathematics RCA0+ISigma_n and ACA0. We exhibit new elements of these sets and conclude that the sets are Pi_2 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.

Cite

@article{arxiv.1302.1488,
  title  = {On Maximum Conservative Extensions},
  author = {Henry Towsner},
  journal= {arXiv preprint arXiv:1302.1488},
  year   = {2013}
}
R2 v1 2026-06-21T23:22:01.744Z