I need this answer within 3 days! I don't know how to designate that.  

My question involves PREVENTION of future mold outbreaks in a concrete
stairwell within a home in Chicago, which is obviously known for cold
winters and warm summers.   I have done some web research on mold
prevention and remediation generally, but I have not found the answer
to two questions, which are specific to CONCRETE residential
construction.

Here are the details: 
I live in the 3rd floor unit of condominium built in the last 18
months.  The building is made of poured concrete, and the ceilings are
concrete forms.  The uppermost units include a rooftop deck, which is
accessed by a stairway that is internal to my unit.  The walls of this
stairway are uninsulated concrete, and it seems they are also not
insulated on the exterior.

Recently we have discovered serious GREEN GROWTH in this area (which
is of course, quite tall), and condensation on the ceiling.   The
developer's proposed solution is to sandblast the current paint, apply
something (either a sealant or a special paint?) to the walls, then
apply polysterene insulation INTERNALLY.

My questions are: 
(1) is the developer's proposed solution likely to work? 
(proposal=application of some substance, followed by insulation)  And
must it also include the ceiling?  On the other hand, is a much more
expensive solution (e.g. exterior insulation) required?

(2) More generally, is a "vapor barrier" called for in this situation,
and, if so, what type?  After my amateur research, I was throwing that
word around liberally with the developer because it had a nice sound
to it (!) and he was nodding his head. But now I'm not so sure,
because the developer's theory is that the problem is created not by
moisture coming in from outside but internally, simply from warm air
from the unit hitting cold air up near ceiling, causing condensation
and then mold growth, so I'm not sure what the v.b. would be keeping
out or in.

Thanks.  MM

If you don't like his solution how do you plan on stopping him?

Here is what I would do:  Let him fix it and see what happens.  The
water is getting there somehow.  You will know very quickly if the
problem is solved.

to just4fun2-ga: 

we will not know very quickly if the problem is solved, because the
problem only occurred in winter and we are coming up on spring/summer!
 Also, if he installs insulation on the inside and then drywall, we
will have no idea what is going on beneath it.  it's not a leak, it's
the formation of condensation that apparently only occurs in cold
weather.

Strikes me that you need some form of ventilation
- or a condensor

You need to remove the water vapour from the system, not just move it around

to boroughmal-ga: 

Wow, I am not at all disappointed; I'm impressed and thankful that you
took the time to make your comments.  And I'm glad the contractor
knows what he is doing...I just didn't want to rely on his opinion....

My only concern is when you say ventilate externally---how oh how, if
the walls are solid concrete?   Through the roof?