On maximum conservative extensions

Article type: Research Article

Authors: Towsner, Henry

Affiliations: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA. E-mail: [email protected]; Url: www.math.upenn.edu/~htowsner

Abstract: We investigate the set of Π12 sentences which are Π11 conservative over theories of second order arithmetic. We exhibit new elements of these sets and conclude that the sets are Π2 complete. Along the way, we show that, over the theory RCA0, induction for Σn formulas has essentially no consequences for Δn+1 formulas.

Keywords: Reverse mathematics, forcing, conservative extensions

DOI: 10.3233/COM-150033

Journal: Computability, vol. 4, no. 1, pp. 57-68, 2015