Mohammad Mahmoud, Pure Mathematics, University of Waterloo
"Torsion-free groups: linear independence and computable categoricity"
We
continue
through
Melnikov's
survey
paper
on
Computable
Abelian
Groups.
We
use
the
effective
analysis
of
linear
independence
(discussed
before
by
Sam)
to
characterize
computable
categoricity.
We
go
through
the
proof
that
"Every
computable
torsion-free
abelian
group
of
infinite
rank
has
a
presentation
(computable)
in
which
linear
independence
is
undecidable".
It
follows
as
a
corollary
from
this
and
an
earlier
proposition
that
"A
computable
torsion-free
abelian
group
is
computably
categorical
iff
its
rank
is
finite".