Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 02 October 2013, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Zhang Jing

Title: Weakly represented families in reverse mathematics.

Abstract:

In this talk, we introduce the notion of a weakly represented family

of sets and functions into principles in Second Order arithmetic in

the context of reverse mathematics. This extends the existing notions

about sequence of sets or functions which are uniformly recursive in a

set of the model. With the help of weakly represented families of sets

and functions, we are able to investigate a larger class of sets or

functions, for example, the class of total recursive functions, the

class of recursive sets etc. Specifically, we investigate the Cohesive

Principle for weakly represented family (COHW) and separate COHW from

Cohesive Principle COH. Further, other related principles using weakly

represented family of sets/functions are also investigated, such as

Domination Principle (DOM), Avoiding Principle (AVOID), Meeting

Principle (MEET) and Hyperimmune Principle (HIM). Our results show

that weakly represented families are a natural and robust notion to

formalize principles in reverse mathematics.

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html