MidWest Model Theory Day

Thursday, April 26th, 2012 at UIC


Speakers: Juliette Kennedy, Cameron Hill, Jouko Väänänen

Schedule: All talks are about an hour long, in SEO 636. There will also be coffee&cookies in 636.
It is probably easiest to park in the university parking lot on Morgan St. between Roosevelt and Taylor.
Let us know (@colum.edu">cshawcolum.edu) if you are planning to come to lunch and/or dinner so we can make approximately correct reservations!

Titles & Abstracts:

Speaker: Juliette Kennedy
Title: Change the Logic, Change the Meaning? Quine's Dictum and the Case of Set Theory.

Abstract: In his 1946 Princeton Bicentennial Lecture Goedel suggested the problem of finding a notion of definability for set theory which is "formalism free" in a sense similar to the notion of computable function --- a notion which is very robust with respect to its various associated formalisms. One way to interpret this suggestion is to consider standard notions of definability in set theory, which are usually built over first order logic, and change the underlying logic. We show that constructibility is not very sensitive to the underlying logic, and the same goes for hereditary ordinal definability (or HOD). We observe that under an extensional notion of meaning for set theoretic discourse, Quine's Dictum "change of logic implies change of meaning" is only partially true. This is joint work with Menachem Magidor and Jouko Vaananen.

Speaker: Cameron Hill
Title: Well-quasi-orders in model-theory

Abstract:
The notion of well-quasi-ordering (w.q.o.) is a mainstay of discrete mathematics, especially structural graph theory, but it has appeared only rarely in the model theory of infinite structures. I will discuss two ways that w.q.o.'s can appear in model theory of locally-finite theories -- a w.q.o. of definable sets, and a w.q.o. of finite submodels -- and how these two kinds of w.q.o.'s can be very closely related in certain ``strongly-locally-finite'' theories. Time permitting, I may also discuss a sense in which the w.q.o.'s that arise in model theory are ``universal'' for all well-quasi-orders that arise in a certain structurally nice way.

Speaker: Jouko Väänänen
Title: Second-Order Logic and Model Theory

Abstract: Second-order logic is so strong that it makes sense to ask, are complete finitely axiomatized second-order theories always categorical? Carnap claimed that the answer is yes, but his proof did not work. Ajtai and Solovay showed that the answer depends on set theory. We present some recent new results in this field. This is joint work with Hyttinen and Kangas.

Organizers:
Uri Andrews
Lynn Scow
Chris Shaw

Other MWMTDs:
April 5th, 2016
October 28th, 2014
October 22nd, 2013
April 18th, 2013
October 23rd, 2012
April 26th, 2012
October 11th, 2011
April 7th, 2011
October 26th, 2010