Computability Theory and its Applications

University Of Chicago, Chicago IL

Investigators

Abstract

In this project, the P.I. studies problems in both pure and applied Computability Theory. The problems in pure computability theory are part of the ongoing program to understand the structure of the Turing Degrees. As for applied computability theory, the P.I. applies methods from computability theory to study the effective content and proof-theoretical strength of various areas of both classical mathematics and foundations of mathematics. He concentrates in problems related to linear orderings, but not exclusively, and also works in effective randomness and computable model theory. Computability Theory is the area of Logic that studies the notion of algorithm. Its applications are based on the idea that problems that can be solved using algorithms are simpler than the ones that cannot. This is used in various ways to measure the complexity of mathematical objects, theorems, sequences of zeros and ones, etc.. It is usually the case that this analysis gives a better understanding of the subject under study.