Characterizing the Join-Irreducible Medvedev Degrees
Shafer, Paul
Notre Dame J. Formal Logic, Tome 52 (2011) no. 1, p. 21-38 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We characterize the join-irreducible Medvedev degrees as the degrees of complements of Turing ideals, thereby solving a problem posed by Sorbi. We use this characterization to prove that there are Medvedev degrees above the second-least degree that do not bound any join-irreducible degrees above this second-least degree. This solves a problem posed by Sorbi and Terwijn. Finally, we prove that the filter generated by the degrees of closed sets is not prime. This solves a problem posed by Bianchini and Sorbi.
Publié le : 2011-01-15
Classification:  Medvedev degrees,  lattices,  Brouwer algebras,  intermediate logics,  03D30,  03G10,  03B55 
@article{1292249608,
     author = {Shafer, Paul},
     title = {Characterizing the Join-Irreducible Medvedev Degrees},
     journal = {Notre Dame J. Formal Logic},
     volume = {52},
     number = {1},
     year = {2011},
     pages = { 21-38},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1292249608}
}

Shafer, Paul. Characterizing the Join-Irreducible Medvedev Degrees. Notre Dame J. Formal Logic, Tome 52 (2011) no. 1, pp.  21-38. http://gdmltest.u-ga.fr/item/1292249608/