Alexander G. Melnikov

Office: INMS 3.05
Address: The Institute of Natural and Mathematical Sciences, Private Bag 102 904 NSMC Albany 0745 AUCKLAND

Academic CV

Click here for my CV.

What's new?

Foundations of online structure theory. Submitted. With Bazhenov, Downey, Harrison-Trainor, and Kalimullin.
Online presentations of finitely generated structures. Submitted. With Bazhenov, Kalimullin, and Ng.
Punctual copies of algebraic structures (in Russian). Submitted. With Frolov, Kalimullin, and Zubkov.
Categorical linearly ordered structures. Submitted. With Downey and Ng.
Enumerating abelian p-groups. Submitted. With Downey and Ng.
Decompositions of decidable abelian groups. Submitted. With Bazhenov and Goncharov.
A difference hierarchy of Arithmetical sets. Submitted. 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.

PhD dissertations

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


Eliminating unbounded search in computable algebra. Lecture Notes in Computer Science book series, volume 10307, Conference on Computability in Europe CiE 2017: Unveiling Dynamics and Complexity, pp 77-87 .
Computable Abelian Groups. The Bulletin of Symbolic Logic, Vol. 20, No. 3 (2014), pp. 315-356.
Computable Model Theory. A book chapter in: Turing's Legacy: Developments from Turing Ideas in Logic, R. Downey, editor, Cambridge University Press (2014), pp. 124-194. With Ekaterina Fokina and Valentina Harizanov.

Journal papers and papers in refereed conference proceedings

Computable torsion abelian groups. Advances in Mathematics, 325 (2018), 864--907. With Ng.
Effectively closed subgroups of the infinite symmetric group. Proceedings of the Amer.Math.Soc, 146 (2018), no. 12, 5421-5435. With Greenberg, Nies, and Turetsky.
Computable topological groups and Pontryagin duality. Transactions of the Amer. Math. Soc., 370 (2018), no. 12, 8709-8737.
Uniform procedures in uncountable structures. The Journal os Symbolic Logic, 83 (2018), no. 2, 529-550. With Greenberg, Knight, and Turetsky.
On a question of Kalimullin. Proceedings of the Amer. Math. Soc., 146 (2018), no. 8, 3553-3563. With Downey and Igusa.
Computable distributive lattices. Sib.Math.J., November 2017, Volume 58, Issue 6, pp 959-970. With Bazhenov, Frolov, and Kalimullin.
Torsion-free abelian groups with optimal Scott families. Journal of Math. Logic, 18 (2018), no. 1, 1850002, 47 pp.
Computable Polish group actions. The Journal of Symbolic Logic, , 83 (2018), no. 2, 443-460. With Montalban.
Structures computable without delay. Theoretical Computer Science, 674 (2017), 73-98.
A Friedberg enumeration of equivalence structures. Journal of Math. Logic., 17 (2017), no. 2, 1750008, 28 pp. With Downey and Ng.
Different versions of categoricity without delay. Algebra and Logic, May 2017, Volume 56, Issue 2, pp 171-177. With Kalimullin and Ng.
On computable field embeddings and difference closed fields. Canadian Journal of Mathematics, 69 (2017), no. 6, 1338-1363. With Miller and Harrison-Trainor.
Computable functors and effective interpretability. The Journal of Symbolic Logic, 82 (1) (2017), 77-97. With Harroson-Trainor, Miller, and Montalban.
Proper divisibility in computable rings. Journal of Algebra, 474 (2017), 180-212. With Greenberg.
Abelian groups and the halting problem. Annals of Pure and Applied Logic, Volume 167, Issue 11, November 2016, Pages 1123-1138. With Downey and Ng.
Comparing Classes of Finite Sums. Algebra i Logika, January 2016, Volume 54, Issue 6, pp 489-501. With Uri Andrews, Dmitriy Dushenin, Cameron Hill, Julia Knight.
Independence in effective algebra. Journal of Algebra, 443 (2015), 441-468. With Montalban and Harrison-Trainor.
On Delta2-categoricity of equivalence relations. Annals of Pure and Applied Logic, 2015, 166(9), pp. 851-880. With Downey and Ng.
Computable Structures and Operations on the Space of Continuous Functions. Fundamenta Mathematicae, 233(2):1-41 (2015). With Keng Meng Ng
Iterated Effective Embeddings of Abelian p-Groups. International Journal of Algebra and Computation,24, 1055 (2014). With Downey and Ng.
Computable Completely Decomposable Groups. Transactions of the American Mathematical Society, Volume 366, Number 8, August 2014, Pages 4243-4266. With Rod Downey.
New Degree Spectra of Abelian Groups. Notre Dame Journal of Formal Logic, 141 (2013), 3275-3289.
Effectively Categorical Abelian Groups. Journal of Algebra, Volume 373, 1 January 2013, Pages 223-248. With Rod Downey.
Limitwise Monotonic Sequences and Degree Spectra of Structures. Proceedings of the American Mathematical Society, 141 (2013), 3275-3289. With Iskander Kalimullin and Bakhadyr Khoussainov.
Computably Isometric Spaces. The Journal of Symbolic Logic, Volume 78, Issue 4 (2013), 1025-1346.
The Classification Problem for Compact Computable Metric Spaces. In Paola Bonizzoni, Vasco Brattka, and Benedikt L{\"o}we, editors, CiE 2013, volume 7921 of Lecture Notes in Computer Science, pages 320--328. Springer, 2013. With Andre Nies.
Randomness and K-triviality in Computable Metric Spaces. Proceedings of the American Mathematical Society, 141 (2013), 2885-2899. With Andre Nies.
Jump Degrees of Torsion-Free Abelian Groups. The Journal of Symbolic Logic, Volume 77, Issue 4 (2012), 1067-1100. With Brooke Andersen, Asher Kach and D. Reed Solomon.
Ulm type, and Coding Rank-Homogeneous Trees in Other Structures. The Journal of Symbolic Logic, Volume 76, Number 3, September 2011, 846-849. With Ekaterina Fokina, Julia F. Knight, C. Maher, and Sara Quinn.
Transforming Trees into Abelian Groups. New Zealand Journal of Mathematics, Vol. 41, (2011), Pages 75-81.
Decidability and Computability of Certain Torsion-Free Abelian Groups. Notre Dame Journal of Formal Logic,, vol 51, number 1, (2010). With Rod Downey, Sergei S. Goncharov, Asher Kach, Julia F. Knight, Oleg V. Kudinov, and Daniel Turetsky.
Computable Ordered Abelian Groups and Fields. In: Programs, Proofs, Processes, Lecture Notes in Computer Science, 2010, Volume 6158/2010, 321-330.
Enumerations and Completely Decomposable Torsion-Free Abelian Groups. Theory Comput. Syst,45(4): 897-916 (2009).

Other writings

Hrushovski constructions and randomizations in computable model theory. A review published in The Bulletin of Symbolic Logic, Volume 19, 2013, page 399.