Vol. 18, No. 3, 1966

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

Robert Arnold Di Paola

Vol. 18 (1966), No. 3, 455–456

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
Received: 14 September 1965
Published: 1 September 1966
Robert Arnold Di Paola