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Finite injury and Σ1-induction

Published online by Cambridge University Press:  12 March 2014

Michael Mytilinaios
Michael Mytilinaios*
Affiliation:
Department of Mathematics and Computer Science, Dartmouth College, Hanover, New Hampshire 03755
*
Department of Mathematics, University of Crete, 71409 Iraklio, Greece
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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 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 1 , March 1989 , pp. 38 - 49
Copyright
Copyright © Association for Symbolic Logic 1989

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References

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