The Journal of Symbolic Logic

Research Article

Finite injury and Σ 1-induction

Michael Mytilinaios 

Department of Mathematics and Computer Science, Dartmouth College, Hanover, New Hampshire 03755

Abstract

Working in the language of first-order arithmetic we consider models of the base theory P . Suppose M is a model of P and let M satisfy induction for Σ 1-formulas. First it is shown that the Friedberg-Muchnik finite injury argument can be performed inside M, and then, using a blocking method for the requirements, we prove that the Sacks splitting construction can be done in M. So, the “amount” of induction needed to perform the known finite injury priority arguments is Σ 1-induction.

(Received March 26 1987)

(Revised July 16 1987)

Correspondence

Department of Mathematics, University of Crete, 71409 Iraklio, Greece