Abstract
AbstractWorking 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 Σ1-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 Σ1-induction.
Publisher
Cambridge University Press (CUP)
Reference11 articles.
1. Simpson S. G. , private correspondence, 05 24, 1984. (Contained the proof of Theorem 3.2 and a discussion of the program.)
2. Kirby L. A. S. , Initial segments of models of arithmetic, Ph.D. thesis, University of Manchester, Manchester, 1977.
3. On the Degrees Less than 0 �
4. The α-finite injury method
5. Some Reasons for Generalizing Recursion Theory
Cited by
31 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献