Professor
Department of Algebra and Mathematical Logic

Kazan Federal University

N.I. Lobachevsky Institute of Mathematics and Mechanics
Volga Region Scientific-Educational Centre of Mathematics

About me
Marat Arslanov

Web of Science (Researcher ID): http://www.researcherid.com/rid/D-7271-2015
Scopus (Author ID): http://www.scopus.com/authid/detail.url?authorId=7004438484
Elibrary (Author ID): http://elibrary.ru/author_items.asp?authorid=6735-2038
ORCID (ORCID ID): http://orcid.org/0000-0001-7773-8394
Google scholar: https://scholar.google.ru/citations?user=97E6sr0AAAAJ&hl=ru&oi=ao

Research Interests

Computability Theory, Degrees of Unsolvability, Turing Degrees, Model Theory

Education

1961-1965Kazan State University,
Faculty of Mechanics and Mathematics

Scientific Degrees and Ranks

1971, Ph.D.Thesis Entitled "On the Structure of Recursively Enumerable Sets"
1988, Sc.D. Thesis Entitled "Completeness in the Arithmetic Hierarchy and ∆-0-2 Sets"
1990, Professor
2016, Member of the Academy of Sciences of the Republic of Tatarstan

Positions

Head of the Department of Algebra and Mathematical Logic, Kazan Federal University, N.I. Lobachevsky Institute of Mathematics and Mechanics
Director of the Volga Region Scientific-Educational Centre of Mathematics , Kazan Federal University

Prizes & Awards

2021, Gold Medal of the S.L. Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk) "For Outstanding Contribution to Mathematics"
2018, Prize of the Academy of Sciences of the Republic of Tatarstan named after Kh.M. Mushtari in Mathematics, Mechanics and Engineering Sciences
2018, Professor of the Year
2014, Medal "For Labour Valour"
2010, Silver Sign of the Seminar "Algebra and Logic"
2010, Honored Professor of Kazan University
2007, Honored Worker of the Higher School of the Russian Federation
2005, Medal "In Commemoration of the 1000th Anniversary of Kazan"
1998, Honored Scientist of the Republic of Tatarstan

Membership in Associations

since 2014, Computability in Europe (Association CiE)
since 2002, European Mathematical Society (EMS)
since 1985, American Mathematical Society (AMS)

Member of Editorial Boards

since 2008, Russian Mathematics (Izvestiya VUZ. Matematika)
since 2007, Asian-European Journal of Mathematics
since 2004, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
since 1998, Lobachevskii Journal of Mathematics
since 1994, Journal of Universal Computer Science
since 1993, Mathematical Logic Quarterly

Additional Information

Chairman of the Dissertation Council D 212.081.24 on Mathematical logic; Algebra; Number Theory; Discrete Mathematics; Mathematical Cybernetics; Mathematical and Software Support for Computers, Complexes and Computer Networks
Leader of the Working Group of the N.I. Lobachevsky Project
Arslanov M.M. Za Streloi Vremeni. Zapiski Kazanskogo Matematika. Kazan, Kazan Federal University (2014), In Russian.

Arslanov M.M., Khisamiev N.G. Sets and Degrees in the Ershov Difference Hierarchy. Ust'-Kamenogorsk, EKSU (2012).

Arslanov M.M., Lempp S. eds. Recursion Theory and Complexity, de Gruyter Series in Logic and Its Applications. Proceedings of the Kazan'97 Workshop, Kazan, Russia, July 14-19, 1997. Walter de Gruyter, Berlin, New York (1999).

Arslanov M.M., Parshin A.N., Shafarevich I.R. eds. Algebra and Analisis. Proceedings of the International Centennial Chebotarev Conference held in Kazan, Russia, June 5-11, 1994. Walter de Gruyter, Berlin, New York (1996).

Arslanov M.M. Local Theory of Degrees of Unsolvability and Δ-0-2 Sets. Kazan, Kazan State University (1987), In Russian.

Arslanov M.M. Recursively Enumerable Sets and Degrees of Unsolvability. Kazan, Kazan State University (1986), In Russian.

2021

Arslanov, M.M., Batyrshin, I.I., Yamaleev, M.M. CEA Operators and the Ershov Hierarchy, (2021) Russian Mathematics, 65 (8), pp. 63-69.

Arslanov, M.M., Yamaleev, M.M.Turing Computability: Structural Theory, (2021) Journal of Mathematical Sciences (United States), 256 (1), pp.1-33.

Arslanov, M.M. Fixed-point Selection Functions, (2021) Lobachevskii Journal of Mathematics, 42 (4), pp. 685-692. 

2019

Akhbari, M.H., Movahedi, F., Arslanov, M. On the Doubly Connected Domination Polynomial of a Graph, (2019) Asian-European Journal of Mathematics, 12 (3), Article No 1950036.

2018

Arslanov, M.M., Yamaleev, M.M. On the Problem of Definability of the Computably Enumerable Degrees in the Difference Hierarchy, (2018) Lobachevskii Journal of Mathematics, 39 (5), pp. 634-638. 

Arslanov, M. Splitting and Non-splitting in the Difference Hierarchy, (2018) Mathematical Structures in Computer Science, 28 (3), pp. 384-391.

2017

Arslanov, M.M., Kalimullin, I.S. A Survey of Results on the d-c.e. and n-c.e. Degrees, (2017) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10010, pp. 469-478.

2016

Arslanov, M.M., Kalimullin, I.S., Yamaleev, M.M. Elementary Theories and Structural Properties of d-c.e. and n-c.e. Degrees, (2016) Lobachevskii Journal of Mathematics, 37 (6), pp. 713-722. 

2015

Arslanov, M.M. Structural Theory of Degrees of Unsolvability: Advances and Open Problems, (2015) Algebra and Logic, 54 (4), pp. 342-346.

2014

Arslanov, M.M. Definable Relations in Turing Degree Structures, (2014) Russian Mathematics, 58 (2), pp. 64-67.

Ehsani, A., Movsisyan, Y., Arslanov, M. A Representation of Paramedial n-ary Groupoids, (2014) Asian-European Journal of Mathematics, 7 (1), Article No 1450020.

2013

Arslanov, M.M. Definable Relations in Turing Degree Structures, (2013) Journal of Logic and Computation, 23 (6), pp. 1145-1154.

2012

Arslanov, M.M. Model-Theoretic Properties of Turing Degrees in the Ershov Difference Hierarchy, (2012) Proceedings of the Steklov Institute of Mathematics, 278 (SUPPL. 1), pp. 57-65. 

Arslanov, M.M. Model-Theoretic Properties of the m-c.e. Degrees, (2012) Journal of Logic and Computation, 22 (4), pp. 669-677. 

2011

Arslanov, M.M., Cooper, S.B., Kalimullin, I.S., Soskova, M.I. Splitting and Nonsplitting in the Σ-0-2 Enumeration Degrees, (2011) Theoretical Computer Science, 412 (18), pp. 1669-1685. 

Arslanov, M.M.The Ershov Hierarchy(2011) Computability in Context: Computation and Logic in the Real World, pp. 49-100.

2010

Arslanov, M.M., Kalimullin, I.Sh., Lempp, S. On Downey's Conjecture, (2010) Journal of Symbolic Logic, 75 (2), pp. 401-441.

2008

Arslanov, M.M., Cooper, S.B., Kalimullin, I.Sh., Soskova, M.I. Total Degrees and Nonsplitting Properties of Σ-0-2 Enumeration Degrees, (2008) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4978 LNCS, pp. 568-578. 

Arslanov, M.M., Batyrshin, I.I., Omanadze, R.Sh. Structural Properties of Q-degrees of n-c. e. Sets, (2008) Annals of Pure and Applied Logic, 156 (1), pp. 13-20. 

Arslanov, M.M., Omanadze, R.S. Q-degrees of n-c.e. Sets, (2008) Illinois Journal of Mathematics, 51 (4), pp. 1189-1206.

2005

Arslanov, M.M., Chong, C.T., Cooper, S.B., Yang, Y. The Minimal e-degree Problem in Fragments of Peano Arithmetic, (2005) Annals of Pure and Applied Logic, 131 (1-3), pp. 159-175.

2004

Arslanov, M., Cooper, S.B., Li, A. There is no Low Maximal d. c. e. Degree - Corrigendum, (2004) Mathematical Logic Quarterly, 50 (6), pp. 628-636.

2003

Arslanov, M.M., Kalimullin, I.S., Cooper, S.B. Splitting Properties of Total Enumeration Degrees, (2003) Algebra and Logic, 42 (1), pp. 1-13.

2002

Arslanov, M., Kehayopulu, N. A Note on Minimal and Maximal Ideals of Ordered Semigroups, (2002) Lobachevskii Journal of Mathematics, 11, pp. 3-6. 

2001

Arslanov, M.M., Kalimullin, I.Sh., Sorbi, A. Density Results in the Δ-0-2 e-degrees, (2001) Archive for Mathematical Logic, 40 (8), pp. 597-614.

2000

Arslanov, M., Cooper, S.B., Li, A. There is no Low Maximal d. c. e. Degree, (2000) Mathematical Logic Quarterly, 46 (3), pp. 409-416.

1998

Arslanov, M.M., Laforte, G.L., Slaman, T.A. Relative Enumerability in the Difference Hierarchy, (1998) Journal of Symbolic Logic, 63 (2), pp. 411-420.

1996

Arslanov, M., Lempp, S., Shore, R.A. Interpolating d-r.e. and REA Degrees Between r.e. Degrees, (1996) Annals of Pure and Applied Logic, 78 (1-3), pp. 29-56.

1995

Arslanov, M.M.Contributions to the History of Variations of Weak Density in the n-r.e. Degrees, (1995) Studies in Logic and the Foundations of Mathematics, 134 (C), pp. 199-208. 

1989

Arslanov, M.M.Completeness in the Arithmetical Hierarchy and Fixed Points, (1989) Algebra and Logic, 28 (1), pp. 1-9.

1987

Arslanov, M.M. The Recursion Theorem, Approximations, and Classifying Index Sets of Recursively Enumerable Sets, (1987) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 278 LNCS, pp. 34-37.

1985

Arslanov, M.M. A Class of Hypersimple Incomplete Sets, (1985) Mathematical Notes of the Academy of Sciences of the USSR, 38 (6), pp. 984-985.

Arslanov, M.M. Effectively Hyperimmune Sets and Majorants, (1985) Mathematical Notes of the Academy of Sciences of the USSR, 38 (2), pp. 677-680.

1969

Arslanov, M.M. On Effectively Hypersimple Sets, (1969) Algebra and Logic, 8 (2), pp. 79-85. 

1968

Arslanov, M.M.Two Theorems on Recursively Enumerable Sets, (1968) Algebra and Logic, 7 (3), pp. 132-134.

Conferences
Here is a list of my recent plenary talks at conferences

2021
Logical Perspectives 2021, Moscow,  Russia, June 7 - July 8, "Definability In The Turing Degree Structures"
Conference of International Mathematical Centers, Sochi, Russia, August 9-13, "On the Structure of the Turing Degrees of Unsolvability"

2020
Second Workshop on Digitalization and Computable Models (WDCM-2020), Novosibirsk, Russia, July 20-24, "Complexity of Fixed-point Selection Functions"
Mal'tsev Meeting 2020, Novosibirsk, Russia, November 16-20, "Relatively Computable Enumerable Degrees and Diagonally Non-computable Functions"

2019
Algebra and Mathematical Logic: Theory and Applications, Kazan, Russia, June 24-28, "DNR Functions and Fixed Point Theorems"

2018
Algebra and Theory of Algorithms, Ivanovo, Russia, March 21-24, "Computability on Reals"
International Algebraic Conference in memory of A.G. Kurosh, Russia, Moscow, May 23-25, "Computability in Real Numbers"




Marat Arslanov

Kazan (Volga Region) Federal University

Volga Region Scientific-Educational Centre of Mathematics

Russian Federation, 35 Kremlevskaya Str., Kazan

Building №14 (unit 2), Office number 502

N.I. Lobachevsky Institute of Mathematics and Mechanics

Department of Algebra and Mathematical Logic  

Email: marat.arslanov@kpfu.ru