# Research

My research area is computable model theory. I am interested in effective properties of mathematical structures and relations on them.

The complete list of my current and past projects:

- Stand-alone Project P27527;
- Elise Richter Project V206;
- Stand-alone Project P23989;
- Lise Meitner Project M1188.

## Peer-reviewed papers

*Computability-theoretic categoricity and Scott families*(with V. Harizanov and D. Turetsky), to appear in Ann. Pure Applied Logic.*Degrees of bi-embeddable categoricity of equivalence structures*(with N. Bazhenov, D. Rossegger and L. San Mauro), to appear in Arch. Math. Logic.*Computable bi-embeddable categoricity*(with N. Bazhenov, D. Rossegger and L. San Mauro), to appear in Algebra Logic.*Bi-embeddability spectra and bases of spectra*(with D. Rossegger and L. San Mauro), to appear in Math. Logic Quarterly.*Measuring the complexity of reductions between equivalence relations*(with D. Rossegger and L. San Mauro), to appear in Computability.*Degree spectra with respect to equivalence relations*(with P. Semukhin and D. Turetsky), to appear in Algebra Logic.*Computable bi-embeddable categoricity of equivalence structures*(with N. Bazhenov,D. Rossegger and L. San Mauro), Proceedings of the 11th Panhellenic Logic Symposium, 2017, 126–132.*Bi-embeddability spectra of structures*(with D. Rossegger and L. San Mauro), Proceedings of the 11th Panhellenic Logic Symposium, 2017, 32–38.*Reducibility and bi-reducibility spectra of equivalence relations*(with D. Rossegger and L. San Mauro), Proceedings of the 11th Panhellenic Logic Symposium, 2017, 83–89.*Linear orders realized by c.e. equivalence relations*(with B. Khoussainov, P. Semukhin and D. Turetsky), J. Symb. Logic, 81 (2016), 463–482.*Categoricity spectra for rigid structures*(with A. Frolov and I. Kalimullin), Notre Dame J. Formal Logic, 57 (2016), 45–57.*Index sets for n-decidable structures categorical relative to m-decidable presentations*(with S. Goncharov, V. Harizanov, O. Kudinov, and D. Turetsky), Algebra Logic, 54 (2015), 520–528 (in Russian), 336–341 (English translation).*Classes of structures with universe a subset of \omega_1*(with S. Friedman, J. Knight, and R. Miller), J. Logic Computation 23 (2013) 6, 1249-1265.*Equivalence relations that are \Sigma^0_3 complete for computable reducibility*(with S. D. Friedman and A. Nies), Lecture Notes in Computer Science 7456 (2012) 26-33.*On \Sigma^1_1 equivalence relations over the natural numbers*(with S. D. Friedman), Math. Logic Quarterly, 58 (2012), 113-124.*Isomorphism relations on computable structures*(with S. D. Friedman, V. Harizanov, J. Knight, C. McCoy, A. Montalbán, J. Symbolic Logic, 77 (2012), 122-132.*Computable embedding problem*(with J. Carson, V. Harizanov, J. F. Knight, S. Quinn, C. Safranski, J. Wallbaum), Algebra Logic, 50 (2012), 478-493.*Classes of Ulm type and coding rank-homogeneous trees in other structures*(with J. F. Knight, A. Melnikov, S. Quinn, C. Safranski), J. Symbolic Logic 76 (2011), 846-869.*The effective theory of Borel equivalence relations*(with S. D. Friedman, A. Törnquist), Ann. Pure Applied Logic, 161 (2010), 837--850.*Degrees of categoricity of computable structures*(with I. Kalimullin and R. Miller), Arch. Math. Logic, 49 (2010), 51--67.*Equivalence relations on classes of computable structures*(with S. D. Friedman), the Proceedings of the Conference of Computability in Europe 2009, Heidelberg, Germany, July 2009, LNSC 5635 (2009), 198-207.*Intrinsic bounds on complexity and definability at limit levels*(with J. Chisholm, S. S. Goncharov, V.S. Harizanov, J. F. Knight, S. Miller), to appear in J. Symbolic Logic.*Index sets for some classes of structures*, Ann. Pure Applied Logic, 157 (2009), 139--147.*Algorithmic properties of structures for the languages with two unary functional symbols*, Logic and Theory of Algorithms, Local Proceedings of CiE'08, 2008, pp. 127-136.*Algorithmic properties of structures for the languages with two unary functional symbols*, Vestnik NGU, 8 (2008), no. 1, pp. 90-101 (in Russian).*Index sets for classes of high rank structures*(with W. Calvert, S. S. Goncharov, J. F. Knight, O. Kudinov, A. S. Morozov, V. Puzarenko), Journal of Symbolic Logic, 72 (2007), no. 4, pp. 1418-1446.*Index Sets of Computable Structures with Decidable Theories*, Computation and Logic in the Real World - Third Conference of Computability in Europe, CiE 2007, Siena, Italy, June 2007, Proceedings, LNCS, v. 4497, pp. 290-296.*Index sets of decidable structures*, Siberian Mathematical Journal, 48 (2007), no. 5, pp. 939-948.*Arithmetical Turing degrees and categorical theories of computable models*, Mathematical Logic in Asia. Proceedings of the 9th Asian Logic Conference, 2006, pp. 58-69.*On spectra of computable models*, Vestnik NGU, 6 (2006), no.6, pp. 69-73 (in Russian).*On complexity of categorical theories with computable models*, Vestnik NGU, 5 (2005), no.2, pp. 78-86 (in Russian).

## Non-peer-reviewed papers and editorship

- Editor of the Special Issue
*Mind Mechanism Mathematics*, Mathematical Structures in Computer Science, March 2018. *Preface*to the Special Issue*Mind Mechanism Mathematics*, Mathematical Structures in Computer Science, March 2018, 338–339.*Computable model theory*(with V. Harizanov and A. Melnikov), Turing's Legacy: Developments from Turing's ideas in Logic (Edited by R. Downey), ASL Lecture Notes in Logic 42 (2014), 124-194.

My list of publications in pdf.