Finite injury and ∑1-induction

Journal of Symbolic Logic 54 (1):38 - 49 (1989)
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
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DOI 10.2307/2275013
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Marcia Groszek & Tamara Hummel (1998). ∑2-Constructions and I∑1. Annals of Pure and Applied Logic 93 (1-3):83-101.

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