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New Zealand Mathematics Colloquium 2001
December 3-6, 2001
Massey University
Palmerston North, New Zealand |
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Organizers
Dr I. Boglaev, Dr M. Carter, Dr J. Hudson, Dr C. Little (convenor), Ass. Prof R. McLachlan, Ass. Prof C. Lai
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Lattice embeddings into the d.c.e. degrees
by
Guohua Wu
Victoria University of Wellington
Say that (a, d) is an isolation pair
if a is a c.e. degree, d is a d.c.e. degree, a < d and
a bounds all c.e. degrees below d. We prove that there are two
isolation pairs (a1, d1),
(a2, d2), and a c.e. degree c such that
- (1) c is incomparable with d1, d2;
- (2) c cups d1, d2 to 0', caps a1, a2 to 0;
- (3) d1 \cup d2=0', a1 \cap a2=0.
Immediately, {0, c, d1, d2, 0'} is
an M5 embedding. By Harrington-Soare's continuity of
capping degrees, our result also gives an N5 embedding into d.c.e. degrees.
Also by combining our construction with the high permission method,
we have that the lattice S8 can also be embedded into the d.c.e. degrees with
0, 1 preserved.
Date received: July 15, 2001
Copyright © 2001 by the author(s).
The author(s) of this document and the organizers of the conference
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Atlas Mathematical Conference Abstracts.
Document # cahf-04.