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

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.