Feb

2

Fri

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

Mushfeq Khan will speak on amenability and symbolic dynamics.

As usual the seminar is in Keller 314.

Feb

16

Fri

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

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

23

Fri

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

Apr

6

Fri

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 $mathbb R$.

## University of Hawaiʻi at Mānoa 2018