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Embedding finite lattices into the ideals of computably enumerable turing degrees

Published online by Cambridge University Press:  12 March 2014

William C. Calhoun  and
Manuel Lerman
William C. Calhoun
Affiliation:
Department of Mathematics, Computer Science and Statistics, Bloomsburg University, Bloomsburg, PA 17815-1301, USA, E-Mail: wcalhoun@bloomu.edu
Manuel Lerman
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT 06260-3009, USA, E-Mail: mlerman@math.uconn.edu
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Abstract.

We show that the lattice L20 is not embeddable into the lattice of ideals of computably enumerable Turing degrees (ℐ), We define a structure called a pseudolattice that generalizes the notion of a lattice, and show that there is a Π2 necessary and sufficient condition for embedding a finite pseudolattice into ℐ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 4 , December 2001 , pp. 1791 - 1802
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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