Matthew
Harrison-Trainor
Pure
Mathematics
University
of
Waterloo
“Forcing and Atomic Models - Part 2”
Abstract:
The
theorem
AMT
says
that
if
T
is
an
atomic
theory,
then
T
has
an
atomic
model.
We
will
introduce
forcing
to
give
a
conservation
result
over
RCA0:
AMT
is
restricted
Π12-conservative
over
RCA0,
that
is,
any
sentence
of
the
form
∀A(Ω(A)
→
∃BΦ(A,
B)),
where
Ω
is
arithmetic
and
Φ
is
Σ03,
provable
by
AMT
is
already
provable
in
RCA0.
In
particular,
this
will
show
that
AMT
does
not
prove
WKL0,
RT2,
and
a
number
of
other
principles.
Please note the time.