On sets represented by the same formula in distinct consistent axiomatizable Rosser theories

Robert Arnold Di Paola

Vol. 18 (1966), No. 3, 455–456

DOI: 10.2140/pjm.1966.18.455

Abstract

In this note a theorem is proved which includes the following: if T is a consistent, axiomatizable Rosser theory in which all recursive functions of one argument are definable and S is any sentence undecidable in T, then given any pair (d₁,d₂) of re (recursively enumerable) degrees, there is a formula F which represents a set of degree d₁ in T and of degree d₂ in T′ = T(S), the theory obtained from T by adjoining S as a new axiom.

Mathematical Subject Classification

Primary: 02.77

Milestones

Received: 14 September 1965

Published: 1 September 1966