The survey contains a detailed discussion of methods and results in the new emerging area
of online “punctual” structure theory. We also state several open problems.

A structure is automatic if its domain, functions, and relations are all regular languages.
Using the fact that every automatic structure is decidable, in the literature many decision …

We investigate computable metrizability of Polish spaces up to homeomorphism. In this paper
we focus on Stone spaces. We use Stone duality to construct the first known example of a …

We combine computable structure theory and algorithmic learning theory to study learning of
families of algebraic structures. Our main result is a model-theoretic characterization of the …

We study autostability spectra relative to strong constructivizations (SC-autostability spectra).
For a decidable structure is the least degree in the spectrum (if such a degree exists).We …

… NA Bazhenov, "Degrees of categoricity for superatomic Boolean algebras," Algebra and …
NA Bazhenov, "Degrees of autostability relative to strong constructivizations for Boolean …

… NA Bazhenov was partially supported by RFBR, … [5] NA Bazhenov, Degrees of categoricity
for superatomic Boolean algebras. Algebra Logic, vol. 52 … [8] NA Bazhenov, IS Kalimullin, and …

We study algorithmic learning of algebraic structures. In our framework, a learner receives
larger and larger pieces of an arbitrary copy of a computable structure and, at each stage, is …

It is proved that for every computable ordinal α, the Turing degree 0 (α) is a degree of
autostability of some computable Boolean algebra and is also a degree of autostability relative to …

The theory of numberings studies uniform computations for families of mathematical objects.
In this area, computability-theoretic properties of at most countable families of sets $\mathcal…