Midwest Computability Seminar

XXV
Part ix



The Midwest Computability Seminar is meeting remotely in the fall of 2020. The recurring Zoom link is:

https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09

Meeting ID: 997 5433 2165

Passcode: midwest



Panopto video     YouTube video


This session will be held jointly with the Computability Theory and Applications Online Seminar.


DATE: Tuesday, December 8th, 2020

TIME: 3:00 - 4:00 PM Central

SPEAKER: Linda Westrick - The Pennsylvania State University

TITLE:
Luzin's (N) and randomness reflection

ABSTRACT:
We show that a computable real-valued function f has Luzin's property (N) if and only if it reflects Π11-randomness, if and only if it reflects Δ11-randomness relative to Kleene's O, and if and only if it reflects Kurtz randomness relative to Kleene's O.  Here a function f is said to reflect a randomness notion R if whenever f(x) is R-random, then x is R-random as well.  If additionally f is known to have bounded variation, then we show f has Luzin's (N) if and only if it reflects weak-2-randomness, and if and only if it reflects Kurtz randomness relative to 0'.  This links classical real analysis with algorithmic randomness.  Joint with Arno Pauly and Liang Yu.



Past Sessions


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If you haven't been receiving the announcements and would like to be included in the list, send an email to drh@math.uchicago.edu.