Calendar

Feb
2
Fri
Logic seminar: David Ross
Feb 2 @ 2:30 pm – 3:20 pm

This semester the Logic Seminar continues at a new day and time, Fridays at 2:30 in Keller 314.

For the first meeting this Friday I will (probably) speak about _Skolem polynomials_:

Abstract:
Over 100 years ago Hardy proved that a certain large class of real functions
was linearly ordered by eventual domination. In 1956 Skolem asked
whether the subclass of integer exponential polynomials is *well*-ordered
by the Hardy ordering, and conjectured that its order type
is epsilon_0. (This class is the smallest containing 1, x, and closed
under +, x, and f^g.) In 1973 Ehrenfeucht proved that the class is
well-ordered, and since then there has been some progress on the order
type.

The proof of well-ordering is rather remarkable and very short, and I
will attempt to expose it (which is to say, cover it) in the hour.

David Ross

Feb
9
Fri
Logic seminar: Mushfeq Khan
Feb 9 @ 2:30 pm – 3:30 pm

Mushfeq Khan will speak on amenability and symbolic dynamics.
As usual the seminar is in Keller 314.

Feb
16
Fri
Logic seminar: David Webb
Feb 16 @ 2:30 pm – 3:30 pm

Continuing the theme of symbolic dynamics, I will demonstrate a proof of Simpson’s result that “Entropy = Dimension” for N^d and Z^d, and discuss some of Adam Day’s work generalizing these results to amenable groups.

Feb
23
Fri
Logic seminar: Umar Gaffar @ Keller 314
Feb 23 @ 2:30 pm – 3:30 pm

This week Umar Gaffar will give Shelah’s proof of the following result:

Let $\lambda$ be the cardinality of an ultraproduct of finite sets. If $\lambda$ is infinite then $\lambda=\lambda^{\aleph_0}$.

Mar
9
Fri
Logic seminar: Mushfeq Khan
Mar 9 @ 2:30 pm – 3:30 pm
Mar
16
Fri
Logic seminar: Mushfeq Khan
Mar 16 @ 2:30 pm – 3:30 pm
Mar
23
Fri
Logic seminar: Amenability and Symbolic Dynamics @ Keller Hall 314
Mar 23 @ 2:30 pm – 3:30 pm

David Webb will continue to discuss results from Adam Day’s paper on amenability and symbolic dynamics.

Apr
6
Fri
Logic seminar: David Ross
Apr 6 @ 2:30 pm – 3:30 pm

This week in the Logic Seminar in Keller 314, David Ross will give an easy proof of a slight extension of a result of Lagarias on the Diophantine equation

$$c(1/x_1+cdots+1/x_s)+b/(x_1 x_2cdots x_s)=a$$

The proof will be nonstandard, but really only require a sufficiently-saturated ordered field extension of $mathbb R$.