Journal of Symbolic Logic

Embedding Finite Lattices into the Ideals of Computably Enumerable Turing Degrees

William C. Calhoun and Manuel Lerman

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Abstract

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 $\mathscr{J}$.

Article information

Source
J. Symbolic Logic, Volume 66, Issue 4 (2001), 1791-1802.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746625

Mathematical Reviews number (MathSciNet)
MR1877022

Zentralblatt MATH identifier
1002.03035

JSTOR
links.jstor.org

Citation

Calhoun, William C.; Lerman, Manuel. Embedding Finite Lattices into the Ideals of Computably Enumerable Turing Degrees. J. Symbolic Logic 66 (2001), no. 4, 1791--1802. https://projecteuclid.org/euclid.jsl/1183746625


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