Zhang Jing: Weakly represented families in reverse mathematics

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.

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

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