Embedding Finite Lattices into the Ideals of Computably Enumerable Turing Degrees

Calhoun, William C.; Lerman, Manuel

J. Symbolic Logic, Tome 66 (2001) no. 1, p. 1791-1802 / Harvested from Project Euclid

Résumé

We show that the lattice L$_{20}$ is not embeddable into the lattice of ideals of computably enumerable Turing degrees ($\mathscr{J}$). We define a structure called a pseudolattice that generalizes the notion of a lattice, and show that there is a $\Pi_2$ necessary and sufficient condition for embedding a finite pseudolattice into $\mathscr{J}$.

Publié le : 2001-12-14
Classification:

@article{1183746625,
     author = {Calhoun, William C. and Lerman, Manuel},
     title = {Embedding Finite Lattices into the Ideals of Computably Enumerable Turing Degrees},
     journal = {J. Symbolic Logic},
     volume = {66},
     number = {1},
     year = {2001},
     pages = { 1791-1802},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746625}
}

Calhoun, William C.; Lerman, Manuel. Embedding Finite Lattices into the Ideals of Computably Enumerable Turing Degrees. J. Symbolic Logic, Tome 66 (2001) no. 1, pp.  1791-1802. http://gdmltest.u-ga.fr/item/1183746625/