Adam Gutter, Pure Mathematics, University of Waterloo
"On elementary extensions of Zariski structures"
The
goal
of
this
talk
is
to
prove
that
any
elementary
extension
of
a
Zariski
structure
can
be
viewed
as
a
Zariski
structure
itself.
Combining
this
with
the
results
about
universal
specialisations
from
the
previous
seminar,
we
obtain
that
dimension
is
a
local
property.
On
the
way
to
these
results,
we
introduce
additional
useful
notions,
including
the
locus
of
a
point
over
a
definable
set
and
the
combinatorial
dimension
of
a
tuple
over
a
set.