Finite injury and Σ1-induction

Journal of Symbolic Logic 54 (1):38 - 49 (1989)
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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

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10.2307/2275013

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Citations of this work

Iterated trees and fragments of arithmetic.Yue Yang - 1995 - Archive for Mathematical Logic 34 (2):97-112.

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References found in this work

Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
The α-finite injury method.G. E. Sacks & S. G. Simpson - 1972 - Annals of Mathematical Logic 4 (4):343-367.

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