Finite Injury and $\sum_1$-Induction
Mytilinaios, Michael
J. Symbolic Logic, Tome 54 (1989) no. 1, p. 38-49 / Harvested from Project Euclid
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.
Publié le : 1989-03-14
Classification: 
@article{1183742849,
     author = {Mytilinaios, Michael},
     title = {Finite Injury and $\sum\_1$-Induction},
     journal = {J. Symbolic Logic},
     volume = {54},
     number = {1},
     year = {1989},
     pages = { 38-49},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183742849}
}
Mytilinaios, Michael. Finite Injury and $\sum_1$-Induction. J. Symbolic Logic, Tome 54 (1989) no. 1, pp.  38-49. http://gdmltest.u-ga.fr/item/1183742849/