Abstract/Details

## A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees preserving greatest element

Englert, Burkhard.
University of Connecticut ProQuest Dissertations Publishing,  2000. 9984065.

### Abstract (summary)

We present a necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable (c.e.) degrees preserving greatest element. In the earlier work Lerman [19] gave a necessary and sufficient condition for embeddings of principally decomposable lattices into the c.e. degrees that do not preserve greatest element. Here, we present the construction of an embedding of a principally decomposable lattice that preserves greatest element, prove that Lerman's condition is sufficient for such an embedding construction and show that the necessity of the condition follows from [19].

### Indexing (details)

Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Computably enumerable degrees; Embedding; Finite lattices; Necessary and sufficient condition; Principally decomposable
Title
A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees preserving greatest element
Author
Englert, Burkhard
Number of pages
74
Degree date
2000
School code
0056
Source
DAI-B 61/08, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
978-0-599-90407-1
Lerman, M.
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9984065
ProQuest document ID
304624195