IMS Graduate Summer School in Logic
(27 Jun - 15 Jul 2016)

~ Abstracts ~


Index sets of structures that are autostable relative to strong constructivizations
Margarita Marchuk, Sobolev Institute of Mathematics, Russian Federation

We obtain exact estimate for the algorithmic complexity for the class of computable models of nontrivial signature, that have a strong constructivization and are autostable relative to strong constructivizations.
And also we obtain exact estimates for the algorithmic complexity for the classes of strongly constructivizable computable models autostable relative to strong constructivizations and belonging to the following natural classes: Boolean algebras, distributive lattices, rings, commutative semigroups, partial orders, linear orders, structures with two equivalences, groups.

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Enumerable functors
Dino Rossegger, Vienna University of Technology, Austria

In computable structure theory one studies the algorithmic complexity of mathematical structures. Many different notions of algorithmic complexity have been developed in this field and often it is interesting to compare structures with respect to these notions. This is usually done by giving reductions between structures or even between classes of structures.

In my talk I will present our results on a new notion of reduction between structures we investigated, enumerable functors, a notion closely related to the recently investigated notion of computable functors.

We showed that enumerable functors are equivalent to effective interpretability when we restrict the equivalence relation in the definition to be $\Delta^0_1$-definable, that enumerable functors preserve $\Sigma_n$-spectra, and that enumerable functor are a stronger notion of reduction than computable functors in the sense that the existence of an enumerable functor between structures always implies the existence of a computable functor but not vice versa. Joint work with Ekaterina Fokina.

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Definable amenable groups in o-minimal structures
Ningyuan Yao, Fudan University, China

In this talk, I will introduce definable groups in o-minimal structures briefly, and focus on torsion free groups and compact groups. Instead of details proof, I will give very simple examples to illustrate the notations, definitions, and results appear in this talk.

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