MidWest Model Theory Day
Thursday, April 26th, 2012 at UIC
Speakers: Juliette Kennedy, Cameron Hill, Jouko Väänänen
All talks are about an hour long, in SEO 636.
There will also be coffee&cookies in 636.
- 11am: Meet on the first floor of SEO if you're already here. We will leave to lunch at 11:20.
- 11:30am: Lunch at Joy Yee's
- 1pm: One talk
- 2:30: Two talk
- 4pm: Three talk
- 5:30pm: Dinner at TBA
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
Speaker: Cameron Hill
Title: Well-quasi-orders in model-theory
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.
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