Two particularly popular, completely virtual logic seminars:

- Online Logic Seminar organized by Wesley Calvert,
- Computability Theory and Applications Online Seminar organized by Brattka, Dzhafarov, Fokina, Greenberg, Kihara, Patey, Pauly and Westrick.

We have a joint seminar with other Midwestern logic groups (the Midwest Computability Seminar) every other week starting August 18, and local seminars on the other Tuesdays, with occasional joint meetings with the Midwest Model Theory Seminar.

The **recurring Zoom link for the Midwest Computability Seminar** is:

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

Meeting ID: 997 5433 2165, Passcode: midwest

The **recurring Webex link for the Midwest Model Theory Seminar** is:

Meeting number: 126 772 4675, Password: (the password is stable, but ask me if you don't have it)

The **recurring Zoom link for the local UW logic seminar** is:

https://uwmadison.zoom.us/j/97091300913?pwd=ZnlEaHovT0ZDbUxLWHFrc2VXSzJOdz09.

Meeting ID: 970 9130 0913, Passcode: 926119

- 8/18/2020 3PM (Midwest Computability Seminar),
Joe Miller,
UW

Title: Redundancy of information: lowering effective dimensionAbstract: A natural way to measure the similarity between two infinite binary sequences X and Y is to take the (upper) density of their symmetric difference. This is the Besicovitch distance on Cantor space. If d(X,Y) = 0, then we say that X and Y are coarsely equivalent. Greenberg, Miller, Shen, and Westrick (2018) proved that a binary sequence has effective (Hausdorff) dimension 1 if and only if it is coarsely equivalent to a Martin-Löf random sequence. They went on to determine the best and worst cases for the distance from a dimension t sequence to the nearest dimension s>t sequence. Thus, the difficulty of increasing dimension is understood.Greenberg et al. also determined the distance from a dimension 1 sequence to the nearest dimension t sequence. But they left open the general problem of reducing dimension, which is made difficult by the fact that the information in a dimension s sequence can be coded (at least somewhat) redundantly. Goh, Miller, Soskova, and Westrick recently gave a complete solution.

I will talk about both the results in the 2018 paper and the more recent work. In particular, I will discuss some of the coding theory behind these results. No previous knowledge of coding theory is assumed.

- 8/25/2020 3PM (Midwest Model Theory Seminar),
Nick Ramsey,
University of California-Los Angeles

Title: Model-theoretic tree propertiesAbstract: The first model-theoretic tree properties were introduced by Shelah as a by-product of his analysis of forking in stable theories. Since then, other tree properties have appeared and, together, these combinatorial dividing lines (TP, TP_{1}/SOP_{2}, TP_{2}, SOP_{1}, etc.) serve as the basis for a growing body of research in model theory. I'll survey the work done in this area (and try to justify the idea that it can be understood as an area) by explaining three of the core ingredients in the theory developed so far: generalized indiscernibles, dividing at a generic scale, and amalgamation. - 9/1/2020 3PM (Midwest Computability Seminar),
Patrick Lutz,
University of California-Berkeley

Title: Part 1 of Martin's Conjecture for order preserving functionsAbstract: Martin's Conjecture is an attempt to make precise the idea that the only natural functions on the Turing degrees are the constant functions, the identity, and transfinite iterates of the Turing jump. The conjecture is typically divided into two parts. Very roughly, the first part states that every natural function on the Turing degrees is either eventually constant or eventually increasing and the second part states that the natural functions which are increasing form a well-order under eventual domination, where the successor operation in this well-order is the Turing jump.In the 1980's, Slaman and Steel proved that the second part of Martin's Conjecture holds for order-preserving Borel functions. In joint work with Benny Siskind, we prove the complementary result that (assuming analytic determinacy) the first part of the conjecture also holds for order-preserving Borel functions (and under AD, for all order-preserving functions). Our methods also yield several other new results, including an equivalence between the first part of Martin's Conjecture and a statement about the Rudin-Keisler order on ultrafilters on the Turing degrees.

In my talk, I will give an overview of Martin's Conjecture and then describe our new results.

- 9/8/2020 3PM (Midwester Model Theory Seminar),
Jana
Maříková,
Western Illinois University, Macomb (visiting University of Vienna, Austria)

Title: Quantifier elimination for o-minimal groups expanded by a valuational cutAbstract: We let R be an o-minimal expansion of a group in a language in which Th(R) eliminates quantifiers, and we let C be a valuational cut in R. We show that if nonforking in certain Morley sequences is symmetric, then the theory of R expanded by a predicate for C and a small number of constants eliminates quantifiers. This is a generalization of results on o-minimal fields with convex subrings satisfying some extra conditions such as T-convexity or o-minimality of the residue field. This is joint work with C. F. Ealy. - 9/15/2020 3PM (Midwest Computability Seminar),
Justin Miller,
University of Notre Dame, Indiana

Title: Noncomputable coding, density, and stochasticityAbstract: We introduce the`into`

and`within`

set operations in order to construct sets of arbitrary intrinsic density from any Martin-Löf random. We then show that these operations are useful more generally for working with other notions of density as well, in particular, for viewing Church and MWC stochasticity as a form of density. - 9/22/2020 3PM (local UW logic seminar),
Todor Tsankov,
University of Lyon 1, France

Title: Invariant measures on the space of linear orders on an ℵ_{0}-categorical structureAbstract: Let M be an ℵ_{0}-categorical structure and denote by LO(M) the compact space of linear orders on M. We investigate the probability measures on LO(M) invariant under the natural action of the automorphism group of M and prove, under rather general model-theoretic assumptions, that either M has a definable linear order or LO(M) carries a unique invariant measure (which can be easily and explicitly described). For many structures M, the space LO(M) is the universal minimal flow of the group Aut(M), and our work is in part motivated by a general unique ergodicity question of Angel, Kechris, and Lyons in topological dynamics. Our proof uses techniques from model theory, representation theory, and probability theory, but no special knowledge will be assumed in the talk. I will also provide some background and motivation. This is joint work with Colin Jahel. - 9/29/2020 3PM (Midwest Computability Seminar),
Chris Porter,
Drake University, Des Moines, Iowa

Title: Effective dimension and the intersection of random closed setsAbstract: The connection between the effective dimension of sequences and membership in algorithmically random closed subsets of Cantor space was first identified by Diamondstone and Kjos-Hanssen. In this talk, I highlight joint work with Adam Case in which we extend Diamondstone and Kjos-Hanssen's result by identifying a relationship between the effective dimension of a sequence and what we refer to as the degree of intersectability of certain families of random closed sets (also drawing on work by Cenzer and Weber on the intersections of random closed sets).As we show, (1) the number of relatively random closed sets that can have a non-empty intersection varies depending on the choice of underlying probability measure on the space of closed subsets of Cantor space - this number being the degree of intersectability of a given family of random closed sets - and (2) the effective dimension of a sequence X is inversely proportional to the minimum degree of intersectability of a family of random closed sets, at least one of which contains X as a member. Put more simply, a sequence of lower dimension can only be in random closed sets with more branching, which are thus more intersectable, whereas higher dimension sequences can be in random closed sets with less branching, which are thus less intersectable, and the relationship between these two quantities (that is, effective dimension and degree of intersectability) can be given explicitly.

- 10/6/2020 3PM (local UW logic seminar),
Uri Andrews,
UW

Title: Complexity profiles and the generic Muchnik degreesAbstract: The generic Muchnik degrees, introduced by Schweber, give a way of comparing the computability-theoretic content of uncountable structures. Though obscured slightly by the need for some set-theoretic machinery, I hope to highlight how this notion really gives an easy and natural way to talk about computable structure theory for uncountable structures. I will focus on the tool of complexity profiles.Complexity profiles are a way of measuring, for two structures A generic Muchnik reducible to B, which subsets of A can be defined using B. The complexity profile of A on itself is the natural analog of considering the relatively intrinsically Σ

_{k}sets in A.Using complexity profiles, I will compare three generic muchnik degrees: Cantor space < Baire space < the Borel-complete degree. In particular, I will describe some dichotomy theorems regarding simple expansions of these and describe how to build degrees strictly between them. (Joint work with Joseph S. Miller, Noah Schweber, and Mariya Soskova.)

- 10/13/2020 3PM (Midwest Computability Seminar),
Leszek Kołoziejczyk,
University of Warsaw, Poland

Title: TBAAbstract TBA - 10/20/2020 3PM (Midwest Model Theory Seminar),
Jerry Keisler,
UW

Title: TBAAbstract TBA - 10/27/2020 3PM (Midwest Computability Seminar),
Liling Ko,
University of Notre Dame, Indiana

Title: TBAAbstract TBA - 11/3/2020 3PM (local UW logic seminar),
Vera
Fischer,
University of Vienna, Austria

Title: TBAAbstract TBA - 11/10/2020 3PM (Midwest Computability Seminar),
Paul Shaefer,
University of Leeds, England

Title: TBAAbstract TBA - 11/17/2020 3PM (local UW logic seminar),
Jaap van Oosten,
Utrecht University, Netherlands

Title: TBAAbstract TBA - 11/24/2020 3PM (Midwest Computability Seminar),
Karen Lange,
Wellesley College, Massachusetts

Title: TBAAbstract TBA - 12/1/2020 3PM (local UW logic seminar),
Martín
Hötzel Escardó,
University of Birmingham, England

Title: TBAAbstract TBA - 12/8/2020 3PM (Midwest Computability Seminar),
Linda Brown Westrick,
Pennsylvania State University, State College

Title: TBAAbstract TBA