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Embedding finite lattices into the ideals of computably enumerable Turing degrees
Journal of Symbolic Logic 66 (4):1791-1802 (2001)
Abstract
We show that the lattice L 20 is not embeddable into the lattice of ideals of computably enumerable Turing degrees (J). We define a structure called a pseudolattice that generalizes the notion of a lattice, and show that there is a Π 2 necessary and sufficient condition for embedding a finite pseudolattice into JLinks
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References found in this work
Lattice nonembeddings and initial segments of the recursively enumerable degrees.Rod Downey - 1990 - Annals of Pure and Applied Logic 49 (2):97-119.
A finite lattice without critical triple that cannot be embedded into the enumerable Turing degrees.Steffen Lempp & Manuel Lerman - 1997 - Annals of Pure and Applied Logic 87 (2):167-185.
A necessary and sufficient condition for embedding ranked finite partial lattices into the computably enumerable degrees.M. Lerman - 1998 - Annals of Pure and Applied Logic 94 (1-3):143-180.
A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees.M. Lerman - 2000 - Annals of Pure and Applied Logic 101 (2-3):275-297.
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