Appalachian set theory -- Andreas Blass at Miami U on January 30, 2010

Appalachian set theory

Saturday, January 30, 2010

Registration and morning refreshments 9 - 9:30 a.m.

Lectures 9:30 a.m. - 12:30 p.m. and 2:30 - 6 p.m. with breaks

Miami University in Oxford OH

270 Engineering Building, which is building no. 43 in cell F-3 on this campus map

Andreas Blass : "Ultrafilters and cardinal characteristics of the continuum"

Workshop description

This workshop will be in three approximately equal-sized parts: one part ultrafilters, one part cardinal characteristics of the continuum, and one part connections between ultrafilters and cardinal characteristics. My (present and still subject to change) plans for the three parts are as follows.

In the first part, I would like to decribe several ways of thinking about ultrafilters, coming from combinatorics, topology, and model theory. Then I want to describe some of the connections between ultrafilters and partition theorems. Third, I'll briefly describe some of the structure of the world of ultrafilters --- the Rudin-Keisler ordering, limits, and tensor products. Finally, I'll describe some ultrafilter-related axioms, independent of ZFC, that have been useful in various contexts.

In the second part, I'll describe a few specific cardinal characteristics and connections between them. I'll explain some of the ways that one thinks about these, including Vojtas's ``generalized Galois-Tukey connections'' and Zapletal's ``tame'' characteristics. I'll also introduce the groupwise density number, a non-tame characteristic with rich connections to ultrafilters.

In the last part, I'll explore some of those connections, as well as other results that relate cardinal characteristics of the continuum to cardinals associated with ultrafilters, for example the minimal number of generators of an ultrafilter or the cofinality of an ultrapower. Some of those connections also involve the partition properties and other structural notions discussed in the first part.



Please contact Paul Larson if you need a ride between Cincinnati (airport or bus terminal) and your hotel.


The parking office is aware this event is going on. No one attending the workshop should need a parking permit. If you receive a ticket, please give it to Paul Larson or Richard Ketchersid as soon as possible to get it voided.
  1. Please refer to this marked up map
  2. Flat Lot across from the Business School (Cook Field) --- Short walking distance to the Engineering Building
  3. Flat Lot directly behind the Engineering Building --- Even shorter distance than Cook Field
  4. Parking Garage near and directly the Engineering Building --- there is a charge to park here 50 cents an hour
  5. DO NOT PARK in the Miami Inn parking lot unless you are a registered guest there

Places to eat

Dinner on High Street


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