Research & publications

Computability, logic & algebra

I study computability in its various forms, with a particular focus on computable numberings and hierarchies of sets. My work also spans mathematical logic and algebra.

Research themes
The Ershov hierarchy · Rogers semilattices · Equivalence relations · Lattices and Boolean algebras

Publications

2026–2027

On Computability of Ideal Lattices

Bazhenov, N., Mustafa, M., Yun, S. (2027). In: Brattka, V., Fernau, H., Galeotti, L. (eds) Timeless Machines: Computability Across Eras. CiE 2026. Lecture Notes in Computer Science, vol 16674. Springer, Cham

On computability-theoretic universality of Boolean-valued models

Bazhenov, N., Mustafa. Journal of Computer and System Sciences Date: November 2026 Article: 103821 Volume: Volume 161

On a Computability-Theoretic Approach to Boolean-Valued Models

Bazhenov, N., Mustafa, M. (2026). In: Li, M., Xia, M., Zhang, P. (eds) Theory and Applications of Models of Computation. TAMC 2025. Lecture Notes in Computer Science, vol 16084. Springer, Singapore

2025

On Learning Existentially Definable Subsets in a Computable Structure

Bazhenov, N., Mustafa, M. (2025). In: Beckmann, A., Oitavem, I., Manea, F. (eds) Crossroads of Computability and Logic: Insights, Inspirations, and Innovations. CiE 2025. Lecture Notes in Computer Science, vol 15764. Springer, Cham

On learning down-sets in quasi-orders, and ideals in Boolean algebras

Bazhenov, N., Mustafa, M. Theory Comput Syst 69, 1 (2025)

Elementary Theories of Rogers Semilattices in the Analytical Hierarchy

N. Bazhenov, M. Mustafa. Higher Recursion Theory and Set Theory. March 2025, 1-18

2024

On diagonal functions for equivalence relations

Badaev, S. A., Bazhenov, N. A., Kalmurzayev, B. S. et al. Arch. Math. Logic 63, 259–278 (2024)

On Learning Families of Ideals in Lattices and Boolean Algebras

Bazhenov, N., Mustafa, M. (2024). In: Chen, X., Li, B. (eds) Theory and Applications of Models of Computation. TAMC 2024. Lecture Notes in Computer Science, vol 14637. Springer, Singapore

On Concept Lattices for Numberings

N. Bazhenov, M. Mustafa and A. Nurakunov. in Tsinghua Science and Technology, vol. 29, no. 6, pp. 1642-1650, December 2024

On Arithmetical Numberings in Reverse Mathematics

Bazhenov, N., Fiori-Carones, M., Mustafa, M. (2024). In: Levy Patey, L., Pimentel, E., Galeotti, L., Manea, F. (eds) Twenty Years of Theoretical and Practical Synergies. CiE 2024. Lecture Notes in Computer Science, vol 14773. Springer, Cham

Free bicommutative superalgebras

V. Drensky, N. Ismailov, M. Mustafa, B. Zhakhayev. Journal of Algebra, Volume 652, 2024, Pages 158-187

2023

Representations via differential algebras and equationally Noetherian algebras

A. A. Mikhalev, M. Mustafa, U. Umirbaev. Journal of Algebra, Volume 633, 2023, Pages 814-830, ISSN 0021- 8693

Dominated convergence theorems in Haagerup noncommutative Lp-spaces

Bekjan, T. N., Mustafa, M. Adv. Oper. Theory 8, 34 (2023)

How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy

N. Bazhenov, M. Mustafa, S. Ospichev, L. S. Mauro. Synthese 201, 55 (2023)

2022

On Two Types of Concept Lattices in the Theory of Numberings

N. Bazhenov, M. Mustafa, A. M. Nurakunov. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Theory and Applications of Models of Computation. TAMC 2022. Lecture Notes in Computer Science, vol 13571. Springer, Cham

Computable embeddability for algebraic structures

N. Bazhenov, M. Mustafa. Asian-European Journal of Mathematics. Volume No. 15, Issue No. 07, Article No. 2250126, Year 2022, World Scientific Publishing Co

Rogers semilattices of limitwise monotonic numberings

N. Bazhenov, M. Mustafa, and Z. Tleuliyeva. Math. Log. Quart., 68: 213-226

Identities and Quasi-Identities of Pointed Algebras

A. O. Basheyeva, M. Mustafa, A. M. Nurakunov. Sib Math J 63, 197–205 (2022)

The first-order theory of the computably enumerable equivalence relations in the uncountable setting

U. Andrews, S. Lempp, M. Mustafa, N. D. Schweber. Journal of Logic and Computation, Volume 32, Issue 1, January 2022, Pages 98–114

The algebraic and geometric classification of nilpotent right alternative algebras

N. Ismailov, I. Kaygorodov, M. Mustafa. Period Math Hung 84, 18–30 (2022)

Rogers semilattices of punctual numberings

N. Bazhenov, M. Mustafa, S. Ospichev. Mathematical Structures in Computer Science, 1-25.(2022)

2021

One-Element Rogers Semilattices in the Ershov Hierarchy

S. A. Badaev, B. S. Kalmurzaev, N. Mukash, M. Mustafa. Algebra Logic 60, 284–287 (2021). (Translated from Algebra i Logika, Vol. 60, No. 4, pp. 433-437, July-August, 2021) · Russian version

Theories of Rogers Semilattices of Analytical NumberingsN. Bazhenov, M. Mustafa, Z. Tleuliyeva. Lobachevskii J Math 42, 701–708 (2021)

Approximating Approximate Reasoning: Fuzzy Sets and the Ershov Hierarchy

N. Bazhenov, M. Mustafa, S. Ospichev, L. S. Mauro. In: Ghosh, S., Icard, T. (eds) Logic, Rationality, and Interaction. LORI 2021. Lecture Notes in Computer Science, vol 13039. Springer, Cham

Hardy type inequalities for quaternion-valued functions

M. Mustafa, D. Suragan. V18, N1. Page 338-344 (2021)

Basic Theory of Impulsive Quaternion-Valued Linear Systems

A. Kashkynbayev, M. Mustafa. In: Ashyralyev, A., Kalmenov, T. S., Ruzhansky, M. V., Sadybekov, M. A., Suragan, D. (eds) Functional Analysis in Interdisciplinary Applications—II. ICAAM 2018. Springer Proceedings in Mathematics Statistics, vol 351.(2021), Springer, Cham

On the universal pairs in the Ershov hierarchy

N. Bazhenov, M. Mustafa, S. Ospichev. Siberian Mathematical Journal, 62, 23-31 (2021)

2020

Numberings in the analytical hierarchy

N. Bazhenov , M. Mustafa, S. Ospichev , M. Yamaleev. Algebra Logic 59, 404–407 (2020)

Properties not retained by pointed enrichments of finite lattices

A. O. Basheyeva, M. Mustafa, A. M. Nurakunov. Algebra Univers. 81, 56 (2020)

Classifying equivalence relations in the Ershov hierarchy

N. Bazhenov, M. Mustafa, L. S. Mauro, M. Yamaleev, and A. Sorbi. Arch. Math. Logic 59, 835–864 (2020)

Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies

N. Bazhenov, M. Mustafa, L. S. Mauro, M. Yamaleev. Lobachevskii J Math 41, 145–150 (2020)

Semilattices of Punctual Numberings

Bazhenov N., Mustafa M., Ospichev S. In: Chen, J., Feng, Q., Xu, J. (eds) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science(), vol 12337. Springer, Cham

2019

Sixteenth Asian Logic Conference: an official meeting of the Association for Symbolic Logic

M. Mustafa. Nazarbayev University, Nur-Sultan, Kazakhstan. June 17–21, 2019. The Bulletin of Symbolic Logic, 25(4), 2019. 456-478

Reductions between Types of Numberings

I. Herbert, M. Mustafa, S. Jain, S. Lempp, F. Stephan. Annals of Pure and Applied Logic. Volume 170, Issue 12, 2019, 102716

Elementary theories and hereditary undecidability for semilattices of numberings

N. Bazhenov, M. Mustafa and M. Yamaleev. Arch. Math. Logic (2019) 58: 485--500

Green-type identities for Rockland operators on graded lie groups

M. Mustafa, D. Suragan. Complex Anal. Oper. Theory 13, 959–966 (2019)

Bounded Reducibility for Computable Numberings

N. Bazhenov, M. Mustafa, S. Ospichev. In: Manea F., Martin B., Paulusma D., Primiero G. (eds) Computing with Foresight and Industry. CiE 2019. Lecture Notes in Computer Science, vol 11558.2019. Springer, Cham

Computable Isomorphisms of Distributive Lattices

N. Bazhenov, M. Mustafa, M. Yamaleev. In: Gopal T., Watada J. (eds) Theory and Applications of Models of Computation. TAMC 2019. Lecture Notes in Computer Science, vol 11436. Springer, Cham

2012–2018

A generalisation of the exponential distribution and its applications on modelling skewed data

M. Zubaira, A. Alzaatreh, M. H. Tahir, M. Mansoora and M. Mustafa. Statistical Theory and Related Fields, 2:1, 68-79, 2018

On interpolation of noncommutative symmetric Hardy spaces

T. Bekjan, M. Mustafa. Positivity 21, 1307–1317 (2017)

Boolean algebras realized by c.e. equivalence relations

M. Mustafa, Bazhenov. N, Stephan F, M. Yamaleev. Siberian electronic mathematical reports. Vol. 14, pp. 848–855, 2017

Friedberg numberings in the Ershov hierarchy

S. Badaev, M. Mustafa, A. Sorbi. Arch. Math. Logic 54, 59–73 (2015)

Families Without Minimal Numberings

K. Abeshev, S. Badaev, M. Mustafa. Algebra and Logic 53, 271–286 (2014). (Translated from Algebra and Logika, Vol. 53, No. 4, pp. 427-450, July-August, 2014)

Rogers semilattices of families of two embedded sets in the Ershov hierarchy

S. Badaev, M. Mustafa, S. Andrea. Mathematical Logic Quarterly. -Vol. 58, issue 4-5. -P.366-376. -2012 August

Positive undecidable numberings in the Ershov hierarchy

M. Mustafa, A. Sorbi. Algebra and logic, Vol. 50, N6, pp. 512--525, 2012. (Translated from Algebra and Logika, Vol. 50, No. 6, pp. 759-780, November-December, 2011)

Proceedings & other works

Mathematical Logic, Computability, Complexity, And Randomness

Jorg Brendle, Rod Downey, Sergey S Goncharov, Manat Mustafa, Guohua Wu, Yue Yang. Proceedings Of The 16th Asian Logic Conference And 14th International Conference On Computability, Complexity, And Randomness

Rogers semilattices in the analytical hierarchy: the case of finite families

N. Bazhenov, M. Mustafa. Accepted to XVI ALC. proceedings