Appalachian set theory

Saturday, April 9, 2016

9:30 a.m. - 6 p.m. with coffee and lunch breaks

Virginia Commonwealth University

Lectures in Temple 1165

Itay Neeman : "Forcing with countable conditions"

Description

The workshop will cover forcing techniques used in the proof that consistently every two ℵ₂-dense real order types are isomorphic.

The question is related to the quest for higher analogues for applications of the proper forcing axiom (PFA). It was raised by Baumgartner in the early 1970s, when he proved the analogous result at ℵ₁. Baumgartner's result at ℵ₁ is a central consequence of PFA (though it precedes the formulation of PFA by almost a decade) and moreover the methods of his proof have been instrumental for other key applications of PFA.

Projected topics include countable reflection of clubs, sparse sets, and iteration theory for countably closed forcing with side conditions.

Suggested reading

The main reference, which covers most of the prerequisites:

• Itay Neeman, Forcing with sequences of models of two types, Notre Dame J. Formal Logic, vol. 55 (2014), pp. 265–298.

For background reading:

• Uri Abraham, Matatyahu Rubin & Saharon Shelah , On the consistency of some partition theorems for continuous colourings, and the structure of ℵ₁-dense real order types, Annals of Pure and Applied Logic vol. 29 (1985), pp. 123–206.
• James Baumgartner, All ℵ₁-dense sets of reals can be isomorphic, Fund. Math. vol 79 (1973), pp. 101-106.
• Sy Friedman, Forcing with finite conditions, Set Theory: Centre de Recerca Matematica, Barcelona, 2003-2004, Trends in Mathematics, Birkhäuser Verlag, pp. 285-295, 2006.
• William Mitchell, I[ω₂] can be the nonstationary ideal on Cof(ω₁), Trans. Amer. Math. Soc. vol. 361 (2009), pp. 561–601.
• Justin Tatch Moore and Stevo Todorcevic, Baumgartner's isomorphism problem for ℵ₂-dense suborders of ℝ, to appear in Archive for Mathematical Logic.

Local information

The nearest airport is Richmond International Airport.

There is no bus service to or from the airport on Friday evening or during the weekend. Transport options include taxis and various shuttle services, see Richmond airport ground transportation page and Virginia Airlink.

A campus map is here, the Temple Building is marked as "117" and its address is 901 West Main Street. Walking directions from the hotel to the Temple Building are here.

Lodging

A block of rooms at a special conference rate ($113.00 + 13.3% tax per night) has been set aside at the Holiday Inn Express Richmond - Downtown. To make a reservation at the conference rate use the group code AST. Reservations can be made online or by calling 804 7881600. Please note that the cutoff date for making a rservation at the special rate is Friday March 18!

The code only works for bookings which are contained in the "window" from April 7 to April 11. If you want a stay which is not contained in the window then probably you should make two separate reservations, with the part outside the window charged at the standard rate.

The hotel address is 201 E Cary Street, Richmond, VA 23219.

Participant travel support

Funds provided by the National Science Foundation will be used to reimburse some participant transportation and lodging expenses. Priority will be given to students and 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 the email address appalachiansettheory@gmail.com

• Your name, university affiliation, mailing address, phone number and email address
• Your nationality and visa status
• Your professional status and some additional information:
  • 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