BIMSA > BIMSA Colloquium On Computability over Finite Types
On Computability over Finite Types
Organizers
Tadahisa Funaki , Jinsong Wu
Speaker
Yue Yang
Time
Wednesday, October 29, 2025 5:00 PM - 6:30 PM
Venue
A6-101
Online
Zoom 388 528 9728 (BIMSA)
Abstract
In his paper “On an extension of finitary mathematics which has not yet been used”, Gödel used the concept of computable function of finite simple type, which he considers as finitary, to prove the consistency of classical number theory. However, in his description of the concept “computable function of typet”, he used the phrase “well-defined mathematical procedure” and remarked

The phrase “well-defined mathematical procedure” is to be accepted as having a clear meaning without any further explanation.

In this talk, we will provide one possible rigorous definition of computable functions of finite type, and compare it with the classical definition of computable functions over natural numbers. This talk is based on joint work with Zekun Jia from National University of Singapore, Keng Meng Ng from Nanyang Technological University, Singapore and Nazanin Tavana from Amir Kabir University, Iran.
Speaker Intro
Yang Yue, Bachelor of Mathematics from Peking University, Ph.D. in Mathematics from Cornell University, USA. Currently a Professor in the Department of Mathematics at the National University of Singapore. His main research areas are computability theory and reverse mathematics in mathematical logic.