Publications

Surveys

Foundations of online structure theory, Bull. Symb. Log., 2019, 25:2, 141-181. With Rod Downey, Iskander Kalimullin, and Alexander Melnikov.

Automatic and polynomial-time structures, punctual computability

Online presentations of finitely generated structures, Theor. Comput. Sci., 2020, 844, 195-216. With Iskander Kalimullin, Alexander Melnikov, and Keng Meng Ng.
Automatic and polynomial-time algebraic structures, J. Symb. Log., 2019, 84:4, 1630-1669. With Matthew Harrison-Trainor, Iskander Kalimullin, Alexander Melnikov, and Keng Meng Ng.
Definable subsets of polynomial-time algebraic structures, in Proceedings of CSR-2020 (Lect. Notes Comput. Sci., 12159), 142-154.

Algorithmic learning

Learning families of algebraic structures from informant, Inf. Comput., 2020, 275, article id 104590. With Ekaterina Fokina and Luca San Mauro.

Theory of numberings

On universal pairs in the Ershov hierarchy, Sib. Math. J., 2021, 62:1, 23-31. With Manat Mustafa and Sergei Ospichev.
Numberings in the analytical hierarchy, Algebra Logic, 2020, 59:5, 404-407. With Manat Mustafa, Sergei Ospichev, and Mars Yamaleev.
Semilattices of punctual numberings, in Proceedings of TAMC-2020 (Lect. Notes Comput. Sci., 12337), 1-12. With Manat Mustafa and Sergei Ospichev.
Bounded reducibility for computable numberings, in Proceedings of CiE-2019 (Lect. Notes Comput. Sci., 11558), 96-107. With Manat Mustafa and Sergei Ospichev.
Elementary theories and hereditary undecidability for semilattices of numberings, Arch. Math. Logic, 2019, 58:3-4, 485-500. With Manat Mustafa and Mars Yamaleev.
Rogers semilattices for families of equivalence relations in the Ershov hierarchy, Sib. Math. J., 2019, 60:2, 223-234. With Birzhan Kalmurzaev.

Equivalence relations and computably enumerable structures

The structure of computably enumerable preorder relations, Algebra Logic, 2020, 59:3, 201-215. With Serikzhan Badaev and Birzhan Kalmurzaev.
Classifying equivalence relations in the Ershov hierarchy, Arch. Math. Logic, 2020, 59:7-8, 835-864. With Manat Mustafa, Luca San Mauro, Andrea Sorbi, and Mars Yamaleev.
Minimal equivalence relations in hyperarithmetical and analytical hierarchies, Lobachevskii J. Math., 2020, 41:2, 145-150. With Manat Mustafa, Luca San Mauro, and Mars Yamaleev.
Weakly precomplete equivalence relations in the Ershov hierarchy, Algebra Logic, 2019, 58:3, 199-213. With Birzhan Kalmurzaev.
Computable isomorphisms of distributive lattices, in Proceedings of TAMC-2019 (Lect. Notes Comput. Sci., 11436), 28-41. With Manat Mustafa and Mars Yamaleev.
On dark computably enumerable equivalence relations, Sib. Math. J., 2018, 59:1, 22-30. With Birzhan Kalmurzaev.
Boolean algebras realized by c.e. equivalence relations, Siberian Electronic Mathematical Reports, 2017, 14, 848-855. With Manat Mustafa, Frank Stephan, and Mars Yamaleev.

Computable embeddings for classes of structures

A note on computable embeddings for ordinals and their reverses, in Proceedings of CiE-2020 (Lect. Notes Comput. Sci., 12098), 1-13. With Stefan Vatev.
Effective embeddings for pairs of structures, in Proceedings of CiE-2019 (Lect. Notes Comput. Sci., 11558), 84-95. With Hristo Ganchev and Stefan Vatev.
Turing computable embeddings, computable infinitary equivalence, and linear orders [pdf download], in Proceedings of CiE-2017 (Lect. Notes Comput. Sci., 10307), 141-151. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-58741-7_15

Computable groups

Decompositions of decidable abelian groups, Int. J. Algebra Comput., 2020, 30:1, 49-90. With Sergey Goncharov and Alexander Melnikov.
The index set of the groups autostable relative to strong constructivizations, Sib. Math. J., 2017, 58:1, 72-77. With Sergey Goncharov and Margarita Marchuk.

HKSS-Universal classes of structures

Computable contact algebras, Fundam. Inform., 2019, 167:4, 257-269.
Categoricity spectra for polymodal algebras, Studia Logica, 2016, 104:6, 1083-1097.

Bi-embeddable structures

Degrees of bi-embeddable categoricity, Computability, 2021, 10:1, 1-16. With Ekaterina Fokina, Dino Rossegger, and Luca San Mauro.
Degrees of bi-embeddable categoricity of equivalence structures, Arch. Math. Logic, 2019, 58:5-6, 543-563. With Ekaterina Fokina, Dino Rossegger, and Luca San Mauro.
Computable bi-embeddable categoricity, Algebra Logic, 2018, 57:5, 392-396. With Ekaterina Fokina, Dino Rossegger, and Luca San Mauro.
Computable bi-embeddable categoricity of equivalence structures, in Proceedings of the 11th Panhellenic Logic Symposium (Delphi, Greece, July 12-16, 2017), 126-132. With Ekaterina Fokina, Dino Rossegger, and Luca San Mauro.

Effective categoricity

Strong degrees of categoricity and weak density, Lobachevskii J. Math., 2020, 41:9, 1630-1639. With Iskander Kalimullin and Mars Yamaleev.
Linear orders and categoricity spectra, in Proceedings of the 14th and 15th Asian Logic Conferences. Singapore: World Scientific, 2019. P. 35-52.
Degrees of categoricity and spectral dimension, J. Symb. Log., 2018, 83:1, 103-116. With Iskander Kalimullin and Mars Yamaleev.
Degrees of autostability for prime Boolean algebras, Algebra Logic, 2018, 57:2, 98-114. With Margarita Marchuk.
Degrees of categoricity for prime and homogeneous models, in Proceedings of CiE-2018 (Lect. Notes Comput. Sci., 10936), 40-49. With Margarita Marchuk.
Computability of distributive lattices, Sib. Math. J., 2017, 58:6, 959-970. With Andrey Frolov, Iskander Kalimullin, and Alexander Melnikov.
Effective categoricity for distributive lattices and Heyting algebras, Lobachevskii J. Math., 2017, 38:4, 600-614.
Degrees of categoricity of rigid structures, in Proceedings of CiE-2017 (Lect. Notes Comput. Sci., 10307), 152-161. With Mars Yamaleev.
A note on effective categoricity for linear orderings, in Proceedings of TAMC-2017 (Lect. Notes Comput. Sci., 10185), 85-96.
Degrees of autostability for linear orders and linearly ordered abelian groups, Algebra Logic, 2016, 55:4, 257-273.
Degrees of categoricity vs. strong degrees of categoricity, Algebra Logic, 2016, 55:2, 173-177. With Iskander Kalimullin and Mars Yamaleev.
The branching theorem and computable categoricity in the Ershov hierarchy, Algebra Logic, 2015, 54:2, 91-104.
Autostability spectra for Boolean algebras, Algebra Logic, 2014, 53:6, 502-505.
Δ⁰₂-categoricity of Boolean algebras, J. Math. Sci., 2014, 203:4, 444-454.
Hyperaritmetical categoricity of Boolean algebras of type B(ω^α×η), J. Math. Sci., 2014, 202:1, 40-49.
Degrees of categoricity for superatomic Boolean algebras, Algebra Logic, 2013, 52:3, 179-187.

Effective categoricity for decidable structures (autostability relative to strong constructivizations)

A note on decidable categoricity and index sets, Siberian Electronic Mathematical Reports, 2020, 17, 1013-1026. With Margarita Marchuk.
Constructing decidable graphs from decidable structures, Algebra Logic, 2019, 58:5, 369-382. With Matthew Harrison-Trainor.
Degrees of autostability relative to strong constructivizations of graphs, Sib. Math. J., 2018, 59:4, 565-577. With Margarita Marchuk.
Autostability spectra for decidable structures, Math. Struct. Comput. Sci., 2018, 28:3, 392-411.
Degrees of autostability relative to strong constructivizations for Boolean algebras, Algebra Logic, 2016, 55:2, 87-102.
The index set of linear orderings that are autostable relative to strong constructivizations [in Russian], Vestnik Novosibirsk. Gos. Univ., Ser. Mat. Mekh. Inform., 2015, 15:3, 51-60. With Sergey Goncharov and Margarita Marchuk. English translation: Index set of linear orderings that are autostable relative to strong constructivizations, J. Math. Sci., 2017, 221:6, 840-848.
Index sets of autostable relative to strong constructivizations constructive models for familiar classes, Dokl. Math., 2015, 92:2, 525-527. With Sergey Goncharov and Margarita Marchuk.
Prime model with no degree of autostability relative to strong constructivizations [pdf download], in Proceedings of CiE-2015 (Lect. Notes Comput. Sci., 9136), 117-126.
The final publication is available at link.springer.com, DOI 10.1007/978-3-319-20028-6_12 .
The index set of Boolean algebras autostable relative to strong constructivizations, Sib. Math. J., 2015, 56:3, 393-404. With Sergey Goncharov and Margarita Marchuk.

The theory of lists

On decidability of list structures, Sib. Math. J., 2019, 60:3, 377-388. With Svetlana Aleksandrova.
Automatic structures and the theory of lists, Siberian Electronic Mathematical Reports, 2015, 12, 714-722.

Boolean algebras with distinguished endomorphisms

Boolean algebras with distinguished endomorphisms and generating trees [in Russian], Vestnik Novosibirsk. Gos. Univ., Ser. Mat. Mekh. Inform., 2015, 15:1, 29-44. English translation: Boolean algebras with distinguished endomorphisms and generating trees, J. Math. Sci., 2016, 215:4, 460-474.
D.c.e. degrees of categoricity for Boolean algebras with a distingushed automorphism [in Russian], Vestnik Novosibirsk. Gos. Univ., Ser. Mat. Mekh. Inform., 2014, 14:1, 19-27. English translation: 2-computably enumerable degrees of categoricity for Boolean algebras with distinguished automorphisms, J. Math. Sci., 2015, 211:6, 738-746.
Computable numberings of the class of Boolean algebras with distinguished endomorphisms, Algebra Logic, 2013, 52:5, 355-366.
Computable categoricity of the Boolean algebra B(ω) with a distinguished automorphism, Algebra Logic, 2013, 52:2, 89-97. With Regina Tukhbatullina.
Constructivizability of the Boolean algebra B(ω) with a distinguished automorphism, Algebra Logic, 2012, 51:5, 384-403. With Regina Tukhbatullina.

Last updated: January 30, 2021.