Speakers

- 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:
**Anand Pillay** - 2:30:
**Noah Schweber** - 4pm:
**Alex Kruckman** - 5:30pm: Dinner at Jaks Tap

It is probably easiest to park in the university parking lot on Morgan St. between Roosevelt and Taylor.

Let us know (jfreitag at uic dot edu) if you are planning to come to lunch and/or dinner so we can make approximately correct reservations!

Anand Pillay

Title: The canonical base property.

Abstract. I will discuss the CBP. And prove that in a certain finite rank environment, rigidity of definable automorphism groups is equivalent to a strong version of the CBP.

The proof is related to old results about 1-based groups. This is joint with Daniel Palacin.

Noah Schweber

Title: Strong reducibilities and counterexamples to Vaught’s conjecture

Abstract: In computable structure theory, the most common method for comparing the complexity of two (countable) structures is Muchnik reducibility: A is Muchnik reducible to B if every copy of B computes a copy of A. This reducibility has been extensively studied; however, its uniform version, Medvedev reducibility — where we demand that the computation be independent of the copy of B chosen — has received much less attention. In this talk, I will present some properties of Medvedev reducibility in the context of counterexamples to Vaught’s conjecture: broadly speaking, if A is a (model of a) counterexample to Vaught’s conjecture, then uniform computations from A have a number of nice combinatorial properties. Moreover, these properties hold for any "reasonably definable” uniform reducibility, not just Medvedev reducibility; and the proofs of these properties rely on large cardinals.

Alex Kruckman

Title: Foundations of cologic

Abstract: The existence of a robust categorical dual to first-order logic is hinted at in (at least) four independent bodies of work: (1) The cologic of profinite groups (e.g. Galois groups), which plays an important role in the model theory of PAC fields [Cherlin - van den Dries - Macintyre, Chatzidakis]. (2) Projective Fraïssé theory [Solecki & coauthors, Panagiotopolous]. (3) Universal coalgebra and coalgebraic logic [Rutten, Kurz - Rosicky, Moss, others]. (4) Ultracoproducts and coelementary classes of compact Hausdorff spaces [Bankston]. In this talk, I will propose a natural syntax and semantics for such a dual "cologic", in which "coformulas" express properties of partitions of "costructures", dually to the way in which formulas express properties of tuples from structures. I will show how the basic theorems and constructions of first-order logic (completeness, compactness, ultraproducts, Henkin constructions, Löwenheim-Skolem, etc.) can be dualized, and I will discuss some possible extensions of the framework.

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