Wednesday, August 15, 2012 4:30 pm
-
4:30 pm
EDT (GMT -04:00)
Paul-Elliot Angles D'Auriac, Université Claude Bernard Lyon 1 and Pure Mathematics, University of Waterloo
"The bounded jump operator"
The
jump
is
an
operator
on
sets
with
nice
properties.
It
is
defined
as
the
halting
set
relativized
to
oracles,
but
this
definition
does
not
take
into
account
how
far
we
use
the
oracle.
This
leads
to
the
fact
that
some
of
these
nice
properties
do
not
hold
for
the
bounded
Turing
reducibility,
such
as
the
Schoenfield
jump
inversion.
We
will
define
another
jump
operator,
the
bounded
jump,
taking
care
of
the
use
of
oracle,
and
prove
that
it
behaves
as
the
counterpart
of
the
jump
for
bounded
reducibility
(the
Schoenfield
jump
inversion
holds)
and
that
the
iterates
of
the
empty
set
by
this
operator
also
recreates
a
hierarchy:
the
Ershov
hierarchy