Embedding finite lattices into the ideals of computably enumerable turing degrees

Author:

Calhoun William C.,Lerman Manuel

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference10 articles.

1. Weinstein B. , On embeddings of the 1-3-1 lattice into the recursively enumerable degrees, Ph.D. thesis , University of California, Berkeley, CA, 1988.

2. A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees

3. Calhoun W. C. , The lattice of ideals of recursively enumerable degrees, Ph.D. thesis , University of California, Berkeley, CA, 1990.

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