Dr Alexander Melnikov staff profile picture

Contact details +64 (09) 414 0800  ext. 43632

Dr Alexander Melnikov

Senior Lecturer in Mathematics

Institute of Natural and Mathematical Sciences

Please see my personal research homepage: 

melnikov.massey.ac.nz

See also my Google Scholar page:

https://scholar.google.com/citations?user=9PbkaUkAAAAJ&hl=en

Research Expertise

Research Interests

Logic, commutative algebra. Please see my personal research homepage 

melnikov.massey.ac.nz

Area of Expertise

Field of research codes
Group Theory and Generalisations (010105): Mathematical Logic, Set Theory, Lattices and Universal Algebra (010107): Mathematical Sciences (010000): Pure Mathematics (010100)

Research Projects

Summary of Research Projects

Position Current Completed
Project Leader 2 0

Research Outputs

Journal

Melnikov, A. (2018). A Friedberg enumeration of equivalence structures. Journal of Mathematical Logic. to appear
[Journal article]Authored by: Melnikov, A.
Melnikov, A. (2018). Computable Topological Groups and Pontryagin Duality. Transactions of the American Mathematical Society. to appear
[Journal article]Authored by: Melnikov, A.
Melnikov, A., & Montalban, A. (2018). Computable Polish group actions. The Journal of Symbolic Logic. To appear
[Journal article]Authored by: Melnikov, A.
Melnikov, A., Harrison-Trainor, M., & Montalban, A. (2017). Computable functors and effective interpretability. The Journal of Symbolic Logic. 82(1), 77-97
[Journal article]Authored by: Melnikov, A.
Melnikov, A., Harrison-Trainor, M., & Montalban, A. (2017). On computable field embeddings and difference closed fields. Canadian Journal of Mathematics. , 1-25 Retrieved from https://cms.math.ca/10.4153/CJM-2016-044-7
[Journal article]Authored by: Melnikov, A.
Kalimullin, IS., Melnikov, AG., & Ng, KM. (2017). The Diversity of Categoricity Without Delay. Algebra and Logic. 56(2), 171-177
[Journal article]Authored by: Melnikov, A.
Kalimullin, I., Melnikov, A., & Ng, KM. (2017). Algebraic structures computable without delay. Theoretical Computer Science. 674, 73-98
[Journal article]Authored by: Melnikov, A.
Greenberg, N., & Melnikov, A. (2017). Proper divisibility in computable rings. Journal of Algebra. 474, 180-212
[Journal article]Authored by: Melnikov, A.
Harrison-Trainor, M., Melnikov, A., Miller, R., & Montalbán, A. (2017). Computable functors and effective interpretability. Journal of Symbolic Logic. 82(1), 77-97
[Journal article]Authored by: Melnikov, A.
Melnikov, AG., & Ng, KM. (2016). Computable structures and operations on the space of continuous functions. Fundamenta Mathematicae. 233(2), 101-141
[Journal article]Authored by: Melnikov, A.
Andrews, U., Dushenin, DI., Hill, C., Knight, JF., & Melnikov, AG. (2016). Comparing Classes of Finite Sums. Algebra and Logic. 54(6), 489-501
[Journal article]Authored by: Melnikov, A.
Downey, R., Melnikov, AG., & Ng, KM. (2016). Abelian p-groups and the Halting problem. Annals of Pure and Applied Logic. 167(11), 1123-1138
[Journal article]Authored by: Melnikov, A.
Downey, R., Melnikov, AG., & Ng, KM. (2015). On δ<sup>0</sup><inf>2</inf>-categoricity of equivalence relations. Annals of Pure and Applied Logic. 166(9), 851-880
[Journal article]Authored by: Melnikov, A.
Harrison-Trainor, M., Melnikov, A., & Montalbán, A. (2015). Independence in computable algebra. Journal of Algebra. 443, 441-468
[Journal article]Authored by: Melnikov, A.
Downey, R., Melnikov, AG., & Ng, KM. (2014). Iterated effective embeddings of abelian p-groups. International Journal of Algebra and Computation. 24(7), 1055-1084
[Journal article]Authored by: Melnikov, A.
Melnikov, AG. (2014). Computable abelian groups. Bulletin of Symbolic Logic. 20(3), 315-356
[Journal article]Authored by: Melnikov, A.
Downey, R., & Melnikov, AG. (2014). Computable completely decomposable groups. Transactions of the American Mathematical Society. 366(8), 4243-4266
[Journal article]Authored by: Melnikov, A.
Melnikov, AG. (2013). Computably isometric spaces. Journal of Symbolic Logic. 78(4), 1055-1085
[Journal article]Authored by: Melnikov, A.
Downey, R., & Melnikov, AG. (2013). Effectively categorical abelian groups. Journal of Algebra. 373, 223-248
[Journal article]Authored by: Melnikov, A.
Kalimullin, I., Khoussainov, B., & Melnikov, A. (2013). Limitwise monotonic sequences and degree spectra of structures. Proceedings of the American Mathematical Society. 141(9), 3275-3289
[Journal article]Authored by: Melnikov, A.
Melnikov, A., & Nies, A. (2013). K-triviality in computable metric spaces. Proceedings of the American Mathematical Society. 141(8), 2885-2899
[Journal article]Authored by: Melnikov, A.
Andersen, BM., Kach, AM., Melnikov, AG., & Solomon, R. (2012). Jump degrees of torsion-free abelian groups. Journal of Symbolic Logic. 77(4), 1067-1100
[Journal article]Authored by: Melnikov, A.
melnikov, A. (2011). Transforming Trees into Abelian Groups. New Zealand Journal of Mathematics.
[Journal article]Authored by: Melnikov, A.
Fokina, E., Knight, JF., Melnikov, A., Quinn, SM., & Safranski, C. (2011). Classes of Ulm type and coding rank-homogeneous trees in other structures. Journal of Symbolic Logic. 76(3), 846-869
[Journal article]Authored by: Melnikov, A.
Melnikov, A., Kach, A., Turetsky, D., Knight, J., Downey, R., Goncharov, S., . . . Kudinov, O. (2010). Decidability and Computability of Certain Torsion-Free Abelian Groups.. Notre Dame Journal of Symbolic Logic.
[Journal article]Authored by: Melnikov, A.
Melnikov, AG. (2009). Enumerations and completely decomposable torsion-free Abelian groups. Theory of Computing Systems. 45(4), 897-916
[Journal article]Authored by: Melnikov, A.

Book

Fokina, E., Harizanov, V., & Melnikov, A. (2014). Computable model theory. In R. Downey (Ed.) Turing's Legacy: Developments from Turing;s ideas in logic. (pp. 124 - 194). : Cambridge University Press
[Chapter]Authored by: Melnikov, A.

Conference

Melnikov, A., & Nies, A. (2013). The classification problem for compact computable metric spaces. Lecture Notes in Computer Science. Vol. 7921 (pp. 320 - 328). : Conference on Computability in Europe CiE 2013: The Nature of Computation. Logic, Algorithms, Applications
[Conference Paper in Published Proceedings]Authored by: Melnikov, A.
Melnikov, A. (2017). Eliminating unbounded search in computable algebra. Lecture notes in computer science. (pp. 77 - 87). : Conference on Computability in Europe, 2017
[Conference Paper in Published Proceedings]Authored by: Melnikov, A.
melnikov, A. (2010). Computable Ordered Abelian Groups and Fields. : Programs, Proofs, Processes
[Conference Paper in Published Proceedings]Authored by: Melnikov, A.

Supervision and Teaching

Summary of Doctoral Supervision

Position Current Completed
CoSupervisor 1 0

Current Doctoral Supervision

CoSupervisor of:

  • Cong Yao - PhD
    Minimisation of mean distortions and Teichmuller Theory

Massey Contact Centre Mon - Fri 8:30am to 5:00pm 0800 MASSEY (+64 6 350 5701) TXT 5222 contact@massey.ac.nz Web chat Staff Alumni News Māori @ Massey