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Finite injury and Σ1-induction
Journal of Symbolic Logic 54 (1):38 - 49 (1989)
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 -inductionOther Versions
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Citations of this work
Fragments of Kripke–Platek set theory and the metamathematics of $$\alpha $$ α -recursion theory.Sy-David Friedman, Wei Li & Tin Lok Wong - 2016 - Archive for Mathematical Logic 55 (7-8):899-924.
The Sacks density theorem and Σ2-bounding.Marcia Groszek, Michael Mytilinaios & Theodore Slaman - 1996 - Journal of Symbolic Logic 61 (2):450 - 467.
∑2 Induction and infinite injury priority arguments, part II Tame ∑2 coding and the jump operator.C. T. Chong & Yue Yang - 1997 - Annals of Pure and Applied Logic 87 (2):103-116.
Iterated trees and fragments of arithmetic.Yue Yang - 1995 - Archive for Mathematical Logic 34 (2):97-112.
The role of true finiteness in the admissible recursively enumerable degrees.Noam Greenberg - 2005 - Bulletin of Symbolic Logic 11 (3):398-410.
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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