MidWest Model Theory Day
Tuesday, October 11th, 2011 at UIC
Speakers: Lou van den Dries, Philipp Hieronymi, Ahuva Shkop
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 Greek Islands
It is probably easiest to park in the university parking lot on Morgan St. between Roosevelt and Taylor.
Let me 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: Philipp Hieronymi
Title: The geometric consequences of not defining the set of integers.
Abstract: Let R be an expansion of the real field that does not define the set of integers. Is there anything (geometrically) that can be said about the sets definable in this expansion (without any further assumptions on R)? A priori, why should non-definability of an arithmetic object translate into a geometric condition on definable sets? In joint work with A. Fornasiero and C. Miller, we established the following metric condition: every nonempty, bounded,
nowhere dense unary set definable in R has Minkowski dimension zero. I will discuss this result (and its proof) and progress towards similar statements for definable sets of higher dimension.
Speaker: Ahuva Shkop
Title: Finding something real in Zilber's field.
Abstract: In 2004, Zilber constructed a class of exponential fields, known as pseudoexponential fields, and proved that there is exactly one pseudoexponential field in every uncountable cardinality up to isomorphism. He conjectured that the pseudoexponential field of size continuum, K , is isomorphic to the classic complex exponential field. Since the complex exponential field contains the real exponential field, one consequence of this conjecture is the existence of a real closed exponential subfield of K . In this talk, I will sketch the proof of the existence of uncountably many non-isomorphic countable real closed exponential subfields of K and discuss some of their properties.
Speaker: Lou van den Dries
Title: Model-theoretic conjectures about transseries
Abstract: This is joint work with Matthias Aschenbrenner
and Joris van der Hoeven. I will introduce the differential field
of transseries, state the main conjecture about it, and show that
other conjectures (asymptotic o-minimality, induced structure
on field of constants, NIP) follow from it.