(panoramic photo of Moscow from moscow.photobase.ru)

# Eighth International Conference on Computability, Complexity and Randomness (CCR 2013)

### September 23–27, 2013, Moscow, Russia

## Nonstandard models of arithmetic and
Ramsey theorem

**Yue Yang**
n this talk, I will start with talking about two seemingly
disjoint areas related to recursion theory. One is to study computability
on weak fragments of arithmetic, whose models are necessarily nonstan-
dard. The other is reverse mathematics, which asks what kind of axioms
are needed in order to prove a mathematical theorem. With a few ex-
ceptions, most of the results in reverse mathematics make use of the
so-called “ω-model”, which has the standard model ω as its first order
part. In the recent study of Ramsey Theorem for pairs, we discovered a
nice application of nonstandard models to reverse mathematics. Using
nonstandard models, we have obtained better understanding of the first
order and second order consequences of combinatorial statements relat-
ed to Ramsey theorem for pairs. This is a joint work with C.T. Chong
and Ted Slaman.