Journal of Symbolic Logic

Finite Injury and $\sum_1$-Induction

Michael Mytilinaios

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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 $\sigma_1$-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 $\Sigma_1$-induction.

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J. Symbolic Logic, Volume 54, Issue 1 (1989), 38-49.

First available in Project Euclid: 6 July 2007

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Mytilinaios, Michael. Finite Injury and $\sum_1$-Induction. J. Symbolic Logic 54 (1989), no. 1, 38--49.

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