Publications
Surveys
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
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
HKSS-Universal classes of structures
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(ωα×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
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.