Boban Velickovic at University of Illinois at Chicago on October 15, 2011
Appalachian set theory
Saturday, October 15, 2011
List of participants in this workshop
Lecture notes by Boban Velickovic and Giorgio Venturi (PDF)
The theory of proper forcing, which has been developed by Shelah over the last
is a powerful tool for proving independence results. However, quite often when
wish to introduce some object by forcing, the obvious partial order is not
In the early 1980s Baumgartner introduced the idea of using side conditions
constrain the way in which the forcing conditions are extended. This approach
later reformulated in terms of finite chains of countable elementary submodels
some H(θ) by Todorcevic and has found numerous applications.
However, in some situations when one wishes to preserve not only ω1 but
also some larger cardinal countable models as side conditions do not suffice and
one is naturally lead to consider side conditions of two or more different
The first such result is due to Mitchell and Friedman who generalized
for adding a club in ω1 to larger cardinals. Recently, the theory of
side conditions has been studied with great success by Neeman who used it to
of the Proper Forcing Axiom for larger cardinals.
In this workshop we present the basic theory of generalized side conditions and
it to obtain several applications such as the Friedman-Mitchell forcing for
adding a thin club to ω2,
Kosmzider's poset for adding a strong ω2-chain of functions in
and the Baumgarther-Shelah poset for adding a thin very tall superatomic Boolean
Some open questions will be discussed at the end of the workshop.
- Uri Abraham, "Proper forcing", in Handbook of set theory
- James Baumgartner,
"Applications of the Proper Forcing Axiom",
in the Handbook of set-theoretic topology,
North-Holland, 1984, pp. 913-959
- James E. Baumgartner and Saharon Shelah, "Remarks on superatomic
Boolean algebras", Annals of Pure and Applied Logic, 1987
- Piotr Koszmider, "On strong chains of uncountable functions",
Israel Journal of Mathematics, 2000
- William J. Mitchell,
"I[ω2] can be the nonstationary ideal
Transactions of the American Mathematical Society
361 (2009) 561-601
Participant travel support
Funds provided by the NSF will be used
to reimburse some participant transportation and lodging expenses.
Priority will be given to students and postdocs,
and to faculty who do not hold federal research grants.
Please request such funds as far in advance of the meeting as possible
by sending the following information to
Ernest Schimmerling by email.
- Your name, university affiliation,
mailing address, phone number and email address
- Your professional status and
- undergraduate students: please describe your background in set theory
- graduate students: please tell us your year and the name of
your thesis advisor if you have one
- faculty: please tell us whether you hold a federal research grant
- A brief statement about your interest in the workshop
- An itemized estimate of your expected transportation expenses
Workshop lectures run from 9:30 a.m. to 6 p.m.
with morning refreshments before the workshop,
starting at around 8:30 or 8:45 a.m.,
several coffee breaks during the workshop,
and a lunch break from 12:30 to 2:30 p.m.
There is no formal dinner but groups of participants will
head out to restaurants after the talks.
- The easiest place to park a car is the
Halsted Street Parking Structure
which is squeezed in between Halsted Street and Expressway 90/94 as
indicated on the map of UIC.
They charge per hour or approximately
$13 for a whole day. It may be cheaper on weekends though.
- The lectures will take place in
Science and Engineering Offices (SEO),
which is easily recognised as the 2nd highest building on campus and
can be found at the center of the map of UIC,
right west of the
parking structure. There are three entrances, but they are all more
or less next to each other.
The lectures themselves will take place in
Room 636 in SEO
which is on the 6th floor of the building.
With lectures beginning at 9:30 AM, the building should be open from
8:30 AM and will close again at 7:00 PM.
- Refreshments will either be offered in 636 or 300 SEO.
There will be some info on the door downstairs and
on 6th floor to indicate where
people should go. The breakfast (the standard fare
including coffee, bagels, fruit, etc) should be ready 45 min - 1 hour
before the first lecture at 9:30.
- Dining: More info will be provided during the conference, but there are
principally three areas for dining around campus; Taylor Street between the
math department and Campus Housing, Halsted Street close to Crowne Plaza,
which is the Greek area, and Halsted Street south of Campus.
For those venturing further away, downtown is easily accessible by
the Blue Line.
- For participants staying at UIC Guest Housing:
- Arriving to O'hare Airport: Most flights arrive to O'hare International
Airport, which is situated at the northwest end of the Blue L-line
(Metro/Subway). To get from the airport to campus housing, by far the
easiest method (other than taxi) is to take the Blue line from O'hare all
the way to the Illinois Medical District stop as indicated on the
Blue Line map.
- Arriving from Midway Airport: Midway Airport is at the end of the Orange
L-line (Metro/Subway), which connects to the Pink Line in downtown (Stop:
State/Lake). Continue on the Pink Line direction 54th/Cermak and get off at
Polk, which is a short walk from Campus Housing.
- Arrival by other public transportation: The Greenhound Station is a short
walk from the UIC HAlsted stop on the Blue L-line (Metro/ Subway). Take this
in the direction of Forest Park and get off at Illinois Medical District, as
indicated on the Blue Line map.
- Getting back and forth to the math department from Campus Housing: There
are several buses and also the Blue L-line connecting the two. These are
indicated on the
Bus 7 map
and Bus 157 map.
Another option is to walk along Taylor Street
directly from the Medical District all the way to the math department.
Taylor Street is pretty busy with many restaurants and cafes, so it is a
reasonably pleasant walk, but takes 30 min.
- Safety: The Medical District and the East Campus, where the math
department is, are in relatively safe areas, but bordered by some bad
neighbourhoods. The stretch between the two on Taylor Street is quite safe
and will be busy on Saturday night, but I would recommend against going
further south down to Roosevelt (see the map), especially at night.
In general, at night it is best to walk in a group and travel on well-lit
streets (Taylor) or alternatively take public transport.