Alexander G. Melnikov

Office: INMS 3.05
Address: The Institute of Natural and Mathematical Sciences, Private Bag 102 904 NSMC Albany 0745 AUCKLAND
Email: alexander.g.melnikov@gmail.com

Academic CV

Click here for my CV which contains full journal references.

What's new?

Enumerating abelian p-groups. Preprint. With Downey and Ng.
Decompositions of decidable abelian groups. Preprint. With Bazhenov and Goncharov.
A difference hierarchy of Arithmetical sets. Preprint. With Selivanov and Yamaleev.
Automatic and polynomial-time algebraic structures. Submitted. With Bazhenov, Harrison-Trainor, Kalimullin, and Ng.
The back-and-forth method and computability without delay. Submitted. With Ng.
The diversity of categoricity without delay. Algebra and Logic. With Kalimullin and Ng.

PhD dissertations

Computability and Structure. PhD dissertation, The University of Auckland.
Effective properties of completely decomposable abelian groups. CSc (PhD) dissertation (in Russian).

Surveys

Eliminating unbounded search in computable algebra. CiE invited paper.
Computable Abelian Groups. The Bulletin of Symbolic Logic.
Computable Model Theory. ASL Lecture Notes in Logic. With Ekaterina Fokina and Valentina Harizanov.

Journal papers and papers in refereed conference proceedings

Computable torsion abelian groups. Advances in Mathematics. With Ng.
Effectively closed subgroups of the infinite symmetric group. Proceedings of the Amer.Math.Soc. With Greenberg, Nies, and Turetsky.
Computable topological groups and Pontryagin duality. Transactions of the Amer. Math. Soc.
Uniform procedures in uncountable structures. The Journal os Symbolic Logic. With Greenberg, Knight, and Turetsky.
On a question of Kalimullin. Proceedings of the Amer. Math. Soc.With Downey and Igusa.
Computable distributive lattices. Sib.Math.J. With Bazhenov, Frolov, and Kalimullin.
A Friedberg enumeration of equivalence structures. Journal of Math. Logic. With Downey and Ng.
Torsion-free abelian groups with optimal Scott families. Journal of Math. Logic
Structures computable without delay. Theoretical Computer Science.
Computable Polish group actions. The Journal of Symbolic Logic. With Montalban.
On computable field embeddings and difference closed fields. Canadian Journal of Mathematics. With Miller and Harrison-Trainor.
Computable functors and effective interpretability. The Journal of Symbolic Logic. With Harroson-Trainor, Miller, and Montalban.
Proper divisibility in computable rings. Journal of Algebra. With Greenberg.
Independence in effective algebra. Journal of Algebra. With Montalban and Harrison-Trainor.
Abelian groups and the halting problem. Annals of Pure and Applied Logic. With Downey and Ng.
On Delta2-categoricity of equivalence relations. Annals of Pure and Applied Logic. With Downey and Ng.
New Degree Spectra of Abelian Groups. Notre Dame Journal of Formal Logic.
Iterated Effective Embeddings of Abelian p-Groups. International Journal of Algebra and Computation. With Downey and Ng.
Comparing Classes of Finite Sums. Algebra i Logika. With Uri Andrews, Dmitriy Dushenin, Cameron Hill, Julia Knight.
Computable Completely Decomposable Groups. Transactions of the American Mathematical Society. With Rod Downey.
Effectively Categorical Abelian Groups. Journal of Algebra. With Rod Downey.
Jump Degrees of Torsion-Free Abelian Groups. The Journal of Symbolic Logic. With Brooke Andersen, Asher Kach and D. Reed Solomon.
Limitwise Monotonic Sequences and Degree Spectra of Structures. Proceedings of the American Mathematical Society. With Iskander Kalimullin and Bakhadyr Khoussainov.
Ulm type, and Coding Rank-Homogeneous Trees in Other Structures. The Journal of Symbolic Logic. With Ekaterina Fokina, Julia F. Knight, C. Maher, and Sara Quinn.
Transforming Trees into Abelian Groups. New Zealand Journal of Mathematics.
Enumerations and Completely Decomposable Torsion-Free Abelian Groups. Theory Comput. Syst.
Decidability and Computability of Certain Torsion-Free Abelian Groups. Notre Dame Journal of Formal Logic. With Rod Downey, Sergei S. Goncharov, Asher Kach, Julia F. Knight, Oleg V. Kudinov, and Daniel Turetsky.
Computable Ordered Abelian Groups and Fields. CiE 2010.
Computable Structures and Operations on the Space of Continuous Functions. Fundamenta Mathematicae. With Keng Meng Ng
Computably Isometric Spaces. The Journal of Symbolic Logic.
The Classification Problem for Compact Computable Metric Spaces. CiE 2013. With Andre Nies.
Randomness and K-triviality in Computable Metric Spaces. Proceedings of the American Mathematical Society. With Andre Nies.

Other writings

Hrushovski constructions and randomizations in computable model theory. A review published in The Bulletin of Symbolic Logic.