The Sacks Density Theorem and $\Sigma_2$-Bounding
Groszek, Marcia J. ; Mytilinaios, Michael E. ; Slaman, Theodore A.
J. Symbolic Logic, Tome 61 (1996) no. 1, p. 450-467 / Harvested from Project Euclid
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The Sacks Density Theorem [7] states that the Turing degrees of the recursively enumerable sets are dense. We show that the Density Theorem holds in every model of $P^- + B\Sigma_2$. The proof has two components: a lemma that in any model of $P^- + B\Sigma_2$, if $B$ is recursively enumerable and incomplete then $I\Sigma_1$ holds relative to $B$ and an adaptation of Shore's [9] blocking technique in $\alpha$-recursion theory to models of arithmetic.
Publié le : 1996-06-14
Classification:  
@article{1183745009,
     author = {Groszek, Marcia J. and Mytilinaios, Michael E. and Slaman, Theodore A.},
     title = {The Sacks Density Theorem and $\Sigma\_2$-Bounding},
     journal = {J. Symbolic Logic},
     volume = {61},
     number = {1},
     year = {1996},
     pages = { 450-467},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745009}
}

Groszek, Marcia J.; Mytilinaios, Michael E.; Slaman, Theodore A. The Sacks Density Theorem and $\Sigma_2$-Bounding. J. Symbolic Logic, Tome 61 (1996) no. 1, pp.  450-467. http://gdmltest.u-ga.fr/item/1183745009/