Michael Deveau, Department of Pure Mathematics, University of Waterloo
"Minimal Pairs of Turineg Degrees"
The
focus
of
this
talk
is
the
construction
of
minimal
pairs
of
certain
classes
of
Turing
degrees,
in
particular
on
the
motivation
behind
two
proofs
involving
minimal
pairs.
First,
I
will
describe
a
naive
construction
of
a
minimal
pair
of
Turing
degrees.
Second,
I
will
present
the
basic
modules
for
the
construction
of
a
minimal
pair
of
computably
enumerable
Turing
degrees,
using
the
ideas
from
the
first
proof
to
motivate
it.
I
will
also
describe
the
technique
of
tree
constructions,
which
is
useful
in
proving
the
latter
result.
This
talk
is
an
outline
of
the
work
that
I
did
for
my
master's
project.
Some
basic
knowledge
of
concepts
from
computability
theory
is
helpful,
but
not
required.