The Midwest Computability
Seminar is a joint venture between the University of Chicago, the University
of Notre Dame, and the University of Wisconsin-Madison. It
meets once or twice per semester at the
University of Chicago, and is attended by faculty and students from these
universities and others
in the area. The seminar started in the
fall of 2008.
DATE: Tuesday, October 9th, 2018.
PLACE: Ryerson Hall 352 (the
Barn), The University of
1100 East 58th Street, Chicago, IL 60637.
- Uri Andrews - University of Wisconsin
- Timothy McNicholl - Iowa State University
- Alexandra Soskova - Sofia University
- 12:30 - 1:30 Lunch
- 1:30 - 2:20 Tim McNicholl
- 2:30 - 3:20 Uri Andrews
- 3:30 - 4:15 Coffee Break
- 4:15 - 5:05 Alexandra Soskova
- 6:00 Dinner at The Nile, 1162 East 55th Street
Title: Strong Jump Inversion
Abstract: We establish a general result with sufficient conditions for a
𝒜 to admit strong jump inversion. We say that a structure
𝒜 admits strong jump inversion provided that for every
oracle X, if X' computes D(𝒞)' for some
𝒞 ≅ 𝒜, then X computes D(ℬ) for
ℬ ≅ 𝒜. C. Jockusch and R. Soare showed that
there are low linear orderings without computable copies, but R. Downey
and C. Jockusch showed that every Boolean algebra admits strong jump
inversion. More recently, D. Marker and R. Miller have shown that all
countable models of DCF0 (the theory of differentially
closed fields of
characteristic 0) admit strong jump inversion. Our conditions involve
an enumeration of B1-types, where these are made up of
are Boolean combinations of existential formulas. Our general result
applies to some familiar kinds of structures, including some classes of
linear orderings and trees, Boolean algebras with no 1-atom, with some
extra information on the complexity of the isomorphism. Our general
result gives the result of D. Marker and R. Miller. In order to apply
our general result, we produce a computable enumeration of the types
realized in models of DCF0. This also yields the fact
saturated model of DCF0 has a decidable copy.
This is a joint work with W. Calvert, A. Frolov, V. Harizanov, J.
Knight, C. McCoy, and S. Vatev.
Title: Effective metric structure theory
Abstract: We will survey recent work on extending the classical computable
structure theory program to uncountable metric structures by means of the
framework of computable analysis. Specifically, we will summarize results
on degrees of categoricity, index sets, and computable presentability for
metric spaces and Banach space, especially Lebesgue spaces.
Title: Recent developments on the structure of ceers
Abstract: We consider the structure of c.e. equivalence relations (ceers)
under computable reduction. That is, if E and R are ceers,
then we say
E ≤ R if and only if there is a computable function
f: ω → ω so that nEm if and only if
This structure is simultaneously reminiscent of the r.e. 1-degrees in some
ways and the r.e. m-degrees in other ways, while having some interesting
unique features of its own. I'll try to give an overview to let you know
what is known about this structure and to point to some of the most
important (purely based on my personal tastes) open problems in this area.
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