Connecticut CT Logic Seminar
The power of uniformity in algorithmic randomness
Jason Rute (Penn State)
Monday, March 10, 2014
It is well known that computable analysis and algorithmic randomness are closely connected. Moreover, computable analysis suggests that uniform reducibility should play a large role in algorithmic randomness. In this talk I will show an application of this insight. I will prove a product theorem for Schnorr randomness for non computable measures. This product theorem is an extension of van Lambalgen's well-known theorem. Both the proof and the statement of the theorem rely heavily on uniformity. It also uses computable analysis in important and insightful ways.