Midwest Computability Seminar

XXVII
Part i


The Midwest Computability Seminar is meeting remotely in the fall of 2021. The recurring Zoom link is:

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

Meeting ID: 997 5433 2165

Passcode: midwest


Rachael Alvir: slides     Panopto video     YouTube video

Josiah Jacobsen-Grocott: slides     Panopto video     YouTube video


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


DATE: Monday, September 13th, 2021

TIME: 3:30 - 4:30 PM Central Time


We will have two speakers:


SPEAKER: Rachael Alvir - University of Notre Dame

TITLE: Finitely α-generated Structures

ABSTRACT: In this talk, we define the notion of a finitely α-generated structure and generalize results about Scott sentences earlier known only for finitely generated structures. We will show how these results can be used to the connect some of the existing non-equivalent definitions of Scott rank.


SPEAKER: Josiah Jacobsen-Grocott - University of Wisconsin

TITLE: A Characterization of the Strongly η-Representable Many-One Degrees

ABSTRACT: η-representations are a way of coding sets in computable linear orders that were first introduced by Fellner in his thesis. Limitwise monotonic functions have been used to characterize the sets with η-representations and give characterizations for several variations of η-representations. The one exception is the class of sets with strong η-representations, the only class where the order type of the representation is unique. We introduce the notion of a connected approximation of a set, a variation on Σ02 approximations. We use connected approximations to give a characterization of the many-one degrees of sets with strong η-representations as well as new characterizations of the variations of η-representations with known characterizations.



Future Sessions

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