Computability Learning Seminar
Jonny Stephenson, Pure Mathematics, University of Waterloo
"Embedding Lattices into the Computably Enumerable Degrees"
The question of which finite lattices can be embedded into the c.e.
degrees first arose with the construction of a minimal pair by Yates,
and independently by Lachlan, showing the 4 element Boolean algebra
can be embedded. This result was rapidly generalised to show any
finite distributive lattice can also be embedded. For non-distributive
lattices, the situation is more complicated.