Marat Faizrahmanov
Chief Researcher
Volga Region Scientific-Educational Centre of Mathematics
Professor
Kazan Federal University, Department of Algebra and Mathematical Logic
Research Interests
Orcid ID: 0000-0002-4519-9696
Researcher ID: K-7976-2015
My Curriculum Vitae
Chief Researcher
Volga Region Scientific-Educational Centre of Mathematics
Professor
Kazan Federal University, Department of Algebra and Mathematical Logic
Research Interests
- Computability Theory
- Theory of Numberings
- Constructive Mathematical Analysis
- Computable Model Theory
- Admissible Sets
Orcid ID: 0000-0002-4519-9696
Researcher ID: K-7976-2015
My Curriculum Vitae
-
Scientific Degrees- 2011, Ph.D. Thesis "Turing Jumps in the Ershov Hierarchy", Kazan State University
- 2020, Sc.D. Thesis "Generalized Computable Numberings and Degree Spectra of Countable Families", S.L. Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk)
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Memberships- Deputy Editor-in-Chief of The Journal of Mathematics and Theoretical Computer Science
- Member of the Working Group of the N.I. Lobachevsky Project
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Education2004-2009, Kazan State University
Faculty of Mechanics and Mathematics -
Additional Information- Professor of the Academy of Sciences of the Republic of Tatarstan
- Member of the Dissertation Council No. 01-03/1325 on defense in 1.1.5. Mathematical logic, algebra, number theory and discrete mathematics
Publications
1. Some Properties of Precompletely and Positively Numbered Sets. Annals of Pure and Applied Logic.176:2 (2025), 103523. 15 pp.
2. Fixed Point Theorems for Minimal Numberings. Journal of Logic and Computation. 35:2 (2025), exad074. 15 pp.
3. A Family Whose Computable Numberings are All Complete. Journal of Logic, Language and Information. 34:1-2 (2025), 155-167.
4. Computable Operators on Left-c.e. Reals and Their Continuity Properties. Logic Journal of the IGPL. 33:3 (2025), jzaf011. 11 pp.
5. Continuity Theorems for a Class of Computable Operators. Mathematical Notes. 117:4 (2025), 591-599.
6. On Infinite Direct Sums of Minimal Numberings of Functional Families. Russian Mathematics. 4 (2025), 38-52 (with Sh. Nodirov and Z. Shchedrikova).
7. An Approach to the Classification of Minimal Numberings of Families of Arithmetical Sets. Siberian Mathematical Journal. 66:2 (2025), 330-338.
8. Control Structures in Computable Numberings and the Completion Operator. Theory of Computing Systems. 69 (2025), 21. 11 pp.
2. Fixed Point Theorems for Minimal Numberings. Journal of Logic and Computation. 35:2 (2025), exad074. 15 pp.
3. A Family Whose Computable Numberings are All Complete. Journal of Logic, Language and Information. 34:1-2 (2025), 155-167.
4. Computable Operators on Left-c.e. Reals and Their Continuity Properties. Logic Journal of the IGPL. 33:3 (2025), jzaf011. 11 pp.
5. Continuity Theorems for a Class of Computable Operators. Mathematical Notes. 117:4 (2025), 591-599.
6. On Infinite Direct Sums of Minimal Numberings of Functional Families. Russian Mathematics. 4 (2025), 38-52 (with Sh. Nodirov and Z. Shchedrikova).
7. An Approach to the Classification of Minimal Numberings of Families of Arithmetical Sets. Siberian Mathematical Journal. 66:2 (2025), 330-338.
8. Control Structures in Computable Numberings and the Completion Operator. Theory of Computing Systems. 69 (2025), 21. 11 pp.
1. Permutation Groups and Ideals of Turing Degrees. Algebra and Logic. 63:2 (2024), 209-224 (with A. Morozov and V. Puzarenko).
2. On Computable Numberings of Families of Turing Degrees. Archive for Mathematical Logic. 63:5-6 (2024), 609-622.
3. On e-principal and e-complete Numberings. Mathematical Notes. 116:3 (2024), 461-476.
4. Some Properties of Classes of Minimal Numberings of Arithmetical Set Families. Math. Theor. Comp. Science. 2:1 (2024), 94-108 (with Sh. Nodirov).
5. Negative Numberings in Admissible Sets. II. Siberian Advances in Mathematics. 34:1 (2024), 41-66 (with I. Kalimullin and V. Puzarenko).
6. A Family with a Single Minimal but Not Least Numbering. Siberian Mathematical Journal. 65:2 (2024), 395-407.
7. On Non-principal Arithmetical Numberings and Families. Theory of Computing Systems. 68:2 (2024), 271-282.
2. On Computable Numberings of Families of Turing Degrees. Archive for Mathematical Logic. 63:5-6 (2024), 609-622.
3. On e-principal and e-complete Numberings. Mathematical Notes. 116:3 (2024), 461-476.
4. Some Properties of Classes of Minimal Numberings of Arithmetical Set Families. Math. Theor. Comp. Science. 2:1 (2024), 94-108 (with Sh. Nodirov).
5. Negative Numberings in Admissible Sets. II. Siberian Advances in Mathematics. 34:1 (2024), 41-66 (with I. Kalimullin and V. Puzarenko).
6. A Family with a Single Minimal but Not Least Numbering. Siberian Mathematical Journal. 65:2 (2024), 395-407.
7. On Non-principal Arithmetical Numberings and Families. Theory of Computing Systems. 68:2 (2024), 271-282.
1. A Local Version of the Slaman-Wehner Theorem and Families Closed Under Finite Differences. Notre Dame J. Form. Logic. 64:2 (2023), 197-203.
2. Numberings, c.e. Oracles, and Fixed Points. Computability. 12:3 (2023), 271-282.
3. Effectively Infinite Classes of Numberings and Computable Families of Reals. Computability. 12:4 (2023), 339-350 (with Z. Shchedrikova).
4. A Classification of Low c.e. Sets and the Ershov Hierarchy. Math. Logic Quart. 69:4 (2023), 508-518.
5. Generalized Computable Numberings and Fixed Points. Math. Theor. Comp. Sci. 1:2 (2023), 35-49.
6. Negative Numberings in Admissible Sets. I. Sib. Adv. Math. 26:1 (2023), 47-92 (with I. Kalimullin and V. Puzarenko).
7. Positive Reducibilities, Extremal Numberings, and Completeness. Sib. Adv. Math. 26:1 (2023), 176-191.
8. Effectively Infinite Classes of Numberings and Fixed Point Theorems. Sib. Electron. Math. Rep. 20:2 (2023), 1519-1536.
9. Two Theorems on Minimal Generalized Computable Numberings. Moscow Univ. Math. Bull. 78:3 (2023), 136-143.
10. On the Embedding of the First Nonconstructive Ordinal in the Rogers Semilattices. Math. Notes. 113:5 (2023), 764-774.
11. Embedding of the First Nonconstructive Ordinal in the Rogers Semilattices of Families of Arithmetic Sets. Sib. Math. J. 64:4 (2023), 830-840.
12. Enumeration Reducibility and Positive Reducibility of the Numberings of Families of Arithmetic Sets. Sib. Math. J. 64:1 (2023), 204-212.
13. Effectively Infinite Classes of Numberings of Computable Families of Reals. Russian Math. 67:4 (2023), 96-100.
2. Numberings, c.e. Oracles, and Fixed Points. Computability. 12:3 (2023), 271-282.
3. Effectively Infinite Classes of Numberings and Computable Families of Reals. Computability. 12:4 (2023), 339-350 (with Z. Shchedrikova).
4. A Classification of Low c.e. Sets and the Ershov Hierarchy. Math. Logic Quart. 69:4 (2023), 508-518.
5. Generalized Computable Numberings and Fixed Points. Math. Theor. Comp. Sci. 1:2 (2023), 35-49.
6. Negative Numberings in Admissible Sets. I. Sib. Adv. Math. 26:1 (2023), 47-92 (with I. Kalimullin and V. Puzarenko).
7. Positive Reducibilities, Extremal Numberings, and Completeness. Sib. Adv. Math. 26:1 (2023), 176-191.
8. Effectively Infinite Classes of Numberings and Fixed Point Theorems. Sib. Electron. Math. Rep. 20:2 (2023), 1519-1536.
9. Two Theorems on Minimal Generalized Computable Numberings. Moscow Univ. Math. Bull. 78:3 (2023), 136-143.
10. On the Embedding of the First Nonconstructive Ordinal in the Rogers Semilattices. Math. Notes. 113:5 (2023), 764-774.
11. Embedding of the First Nonconstructive Ordinal in the Rogers Semilattices of Families of Arithmetic Sets. Sib. Math. J. 64:4 (2023), 830-840.
12. Enumeration Reducibility and Positive Reducibility of the Numberings of Families of Arithmetic Sets. Sib. Math. J. 64:1 (2023), 204-212.
13. Effectively Infinite Classes of Numberings of Computable Families of Reals. Russian Math. 67:4 (2023), 96-100.
1. Families of Permutations and Ideals of Turing Degrees. Algebra and Logic. 61:6 (2022), 706-719 (with A. Morozov and V. Puzarenko).
2. Extremal Numberings and Fixed Point Theorems. Math. Logic Quart. 68:4 (2022), 398-408.
3. On Numberings for Classes of Families of Total Functions. Sib. Adv. Math. 32:4 (2022), 177-197.
4. On p-universal and p-minimal Numberings. Sib. Math. J. 63:2 (2022), 440-449.
5. Splitting of c.e. Degrees and Superlowness. Sib. Electron. Math. Rep. 19:2 (2022), 578-585.
6. One Note on Positive A-computable Numberings. Asian-European J. Math. (2022), 2250218.
2. Extremal Numberings and Fixed Point Theorems. Math. Logic Quart. 68:4 (2022), 398-408.
3. On Numberings for Classes of Families of Total Functions. Sib. Adv. Math. 32:4 (2022), 177-197.
4. On p-universal and p-minimal Numberings. Sib. Math. J. 63:2 (2022), 440-449.
5. Splitting of c.e. Degrees and Superlowness. Sib. Electron. Math. Rep. 19:2 (2022), 578-585.
6. One Note on Positive A-computable Numberings. Asian-European J. Math. (2022), 2250218.
1. Some Properties of the Upper Semilattice of Computable Families of Computably Enumerable Sets. Algebra and Logic. 60:2 (2021), 195-209.
2. Limitwise Monotonic Spectra and Their Generalizations. In: De Mol L., Weiermann A., Manea F., Fernández-Duque D. (eds) CiE 2021. LNCS, V. 12 813. Springer (2021).
3. Absolute and Relative Properties of Negatively Numbered Families. Lobachevskii J. Math. 42:4 (2021), 726-734 (with V. Puzarenko).
4. Weak Reducibility of Computable and Generalized Computable Numberings. Sib. Electron. Math. Rep. 18:1 (2021), 112-120 (with Z. Ivanova).
5. Degrees of Enumerations of Countable Wehner-Like Families. J. Math. Sci. 256:1 (2021), 51-60 (with I. Kalimullin).
2. Limitwise Monotonic Spectra and Their Generalizations. In: De Mol L., Weiermann A., Manea F., Fernández-Duque D. (eds) CiE 2021. LNCS, V. 12 813. Springer (2021).
3. Absolute and Relative Properties of Negatively Numbered Families. Lobachevskii J. Math. 42:4 (2021), 726-734 (with V. Puzarenko).
4. Weak Reducibility of Computable and Generalized Computable Numberings. Sib. Electron. Math. Rep. 18:1 (2021), 112-120 (with Z. Ivanova).
5. Degrees of Enumerations of Countable Wehner-Like Families. J. Math. Sci. 256:1 (2021), 51-60 (with I. Kalimullin).
1. Computable Positive and Friedberg Numberings in Hyperarithmetic. Algebra and Logic. 59:1 (2020), 66-83 (with I. Kalimullin and V. Puzarenko).
2. Semidecidable Numberings in Admissible Sets. Algebra and Logic. 59:3 (2020), 395-402 (with I. Kalimullin and V. Puzarenko).
3. Positive Numberings in Admissible Sets. Sib. Math. J. 61:3 (2020), 607-621 (with I. Kalimullin and V. Puzarenko).
2. Semidecidable Numberings in Admissible Sets. Algebra and Logic. 59:3 (2020), 395-402 (with I. Kalimullin and V. Puzarenko).
3. Positive Numberings in Admissible Sets. Sib. Math. J. 61:3 (2020), 607-621 (with I. Kalimullin and V. Puzarenko).
2019
1. Faizrakhmanov M.Kh. Khutoretskii's Theorem for Generalized Computable Families. Algebra Logika. — 2019. — V. 58, No 4. — P. 528−541.
2. Faizrahmanov M.Kh. Lattice Properties of Rogers Semilattices of Compuatble and Generalized Computable Families. Sib. Electron. Math. Rep. — 2019. — V. 16. — P. 1927−1936.
3. Kalimullin I.Sh., Puzarenko V.G., Faizrahmanov M.Kh. Partial Decidable Presentations in Hyperarithmetic. Sib. Math. J. — 2019. — V. 60, No 3. — P. 599−609.
4. Faizrahmanov M., Kach A., Kalimullin I., Montalban A., Puzarenko V. Jump Inversions of Algebraic Structures and Σ-definability. Math. Log. Quart. — 2019. — V. 65, No 1. — P. 37−45.
2018
1. Kalimullin I.Sh., Puzarenko V.G., Faizrahmanov M.Kh. Positive Presentations of Families Relative to e-oracles. Sib. Math. J. — 2018. — V. 59, No 4. — P. 823−833.
2. Kalimullin I.Sh., Kach A., Montalbán A., Puzarenko, V.G., Faizrakhmanov M.Kh. Jump Inversions of Algebraic Structures and the Σ-definability. Algebra Logika. — 2018. — V. 57, No 2. — P. 243−249.
3. Kalimullin I.Sh., Puzarenko V.G., Faizrakhmanov M.Kh. Positive Presentations of Families in Relation to Reducibility with Respect to Enumerability. Algebra Logika. — 2018. — V. 57, No 4. — P. 492−498.
2017
1. Faizrakhmanov M.Kh. Universal Generalized Computable Numberings and Hyperimmunity. Algebra Logika. — 2017. — V. 56, No 4. — P. 506−521.
2. Faizrahmanov M.Kh. The Rogers Semilattices of Generalized Computable Enumerations. Sib. Math. J. — 2017. — V. 58, No 6. — P. 1418−1427.
3. Faizrahmanov M.Kh. Minimal Generalized Computable Enumerations and High Degrees. Sib. Math. J. — 2017. — V. 58, No 3. — P. 710−716.
4. Faizrahmanov M., Kalimullin I., Montalban A., Puzarenko V. The Least Σ-jump Inversion Theorem for n-families. J. Univ. Comp. Sci. — 2017. — V. 23, No 6. — P. 529−538.
2016
1. Faizrahmanov M., Kalimullin I. The Enumeration Spectrum Hierarchy of n-families. Math. Log. Quart. — 2016. — V. 62, No 4. — P. 420−426.
2. Faizrahmanov M., Kalimullin I. The Enumeration Spectrum Hierarchy of α-families and Low_α Degrees. J. Univ. Comp. Sci. — 2016. — V. 22, No 7. — P. 943−955.
3. Faizrakhmanov M.Kh. Universal Computable Enumerations of Finite Classes of Families of Total Functions. Russian Math. — 2016. — No 12. — P. 96−100.
2015
1. Faizrahmanov M., Kalimullin I. Limitwise Monotonic Sets of Reals. Math. Log. Quart. — 2015. — V. 61, No 3. — P. 224−229.
2. Kalimullin I.Sh., Faizrakhmanov M.Kh. A Hierarchy of Classes of Families and n-low Degrees. Algebra Logika. — 2015. — V. 54, No 4. — P. 536−541.
2014
1. Faizrahmanov M., Kalimullin I., Zainetdinov D. Maximality and Minimality under Limitwise Monotonic Reducibility. Lobachevskii J. Math. — 2014. — V. 35, No 4. — P. 333−338.
2013
1. Faizrahmanov M.Kh. Complements for Enumeration Π-0−1-degrees. Sib. Math. J. — 2013. — V. 54, No 6. — P. 1388−1395.
2012
1. Faizrahmanov M.Kh., Kalimullin I.Sh. Turing and Enumeration Jumps in the Ershov Hierarchy. J. Log. Comput. — 2012. — V. 22, No 4. — P. 737−743.
2. Kalimullin I.Sh., Faizrakhmanov M.Kh. Limitwise Monotonic Spectra of Σ-0−2-sets. Uchen. Zapiski Kazan. Univ.. Seriya Fiz.-Mat. Nauki. — 2012. — V. 154. No 2. — P. 107−116.
2011
1. Faizrakhmanov M.Kh. Turing Jumps in the Ershov Hierarchy. Algebra Logika. — 2011. — V. 50, No 3. — P. 399−414.
2. Faizrakhmanov M.Kh. A Semilattice Generated by Superlow Computably Enumerable Degrees. Russian Math. — 2011. No 1. — P. 85−90.
2010
1. Faizrahmanov M.Kh. Computable Numberings of Families of Low Sets and Turing Jumps in the Ershov Hierarchy. — 2010. Sib. Math. J. — V. 51, No 6. — P. 1435−1439.
2. Faizrakhmanov M.Kh. Decomposability of Low 2-computably Enumerable Degrees and Turing Jumps in the Ershov Hierarchy. Russian Math. — 2010. — No 12. — P. 58−66.
1. Faizrakhmanov M.Kh. Khutoretskii's Theorem for Generalized Computable Families. Algebra Logika. — 2019. — V. 58, No 4. — P. 528−541.
2. Faizrahmanov M.Kh. Lattice Properties of Rogers Semilattices of Compuatble and Generalized Computable Families. Sib. Electron. Math. Rep. — 2019. — V. 16. — P. 1927−1936.
3. Kalimullin I.Sh., Puzarenko V.G., Faizrahmanov M.Kh. Partial Decidable Presentations in Hyperarithmetic. Sib. Math. J. — 2019. — V. 60, No 3. — P. 599−609.
4. Faizrahmanov M., Kach A., Kalimullin I., Montalban A., Puzarenko V. Jump Inversions of Algebraic Structures and Σ-definability. Math. Log. Quart. — 2019. — V. 65, No 1. — P. 37−45.
2018
1. Kalimullin I.Sh., Puzarenko V.G., Faizrahmanov M.Kh. Positive Presentations of Families Relative to e-oracles. Sib. Math. J. — 2018. — V. 59, No 4. — P. 823−833.
2. Kalimullin I.Sh., Kach A., Montalbán A., Puzarenko, V.G., Faizrakhmanov M.Kh. Jump Inversions of Algebraic Structures and the Σ-definability. Algebra Logika. — 2018. — V. 57, No 2. — P. 243−249.
3. Kalimullin I.Sh., Puzarenko V.G., Faizrakhmanov M.Kh. Positive Presentations of Families in Relation to Reducibility with Respect to Enumerability. Algebra Logika. — 2018. — V. 57, No 4. — P. 492−498.
2017
1. Faizrakhmanov M.Kh. Universal Generalized Computable Numberings and Hyperimmunity. Algebra Logika. — 2017. — V. 56, No 4. — P. 506−521.
2. Faizrahmanov M.Kh. The Rogers Semilattices of Generalized Computable Enumerations. Sib. Math. J. — 2017. — V. 58, No 6. — P. 1418−1427.
3. Faizrahmanov M.Kh. Minimal Generalized Computable Enumerations and High Degrees. Sib. Math. J. — 2017. — V. 58, No 3. — P. 710−716.
4. Faizrahmanov M., Kalimullin I., Montalban A., Puzarenko V. The Least Σ-jump Inversion Theorem for n-families. J. Univ. Comp. Sci. — 2017. — V. 23, No 6. — P. 529−538.
2016
1. Faizrahmanov M., Kalimullin I. The Enumeration Spectrum Hierarchy of n-families. Math. Log. Quart. — 2016. — V. 62, No 4. — P. 420−426.
2. Faizrahmanov M., Kalimullin I. The Enumeration Spectrum Hierarchy of α-families and Low_α Degrees. J. Univ. Comp. Sci. — 2016. — V. 22, No 7. — P. 943−955.
3. Faizrakhmanov M.Kh. Universal Computable Enumerations of Finite Classes of Families of Total Functions. Russian Math. — 2016. — No 12. — P. 96−100.
2015
1. Faizrahmanov M., Kalimullin I. Limitwise Monotonic Sets of Reals. Math. Log. Quart. — 2015. — V. 61, No 3. — P. 224−229.
2. Kalimullin I.Sh., Faizrakhmanov M.Kh. A Hierarchy of Classes of Families and n-low Degrees. Algebra Logika. — 2015. — V. 54, No 4. — P. 536−541.
2014
1. Faizrahmanov M., Kalimullin I., Zainetdinov D. Maximality and Minimality under Limitwise Monotonic Reducibility. Lobachevskii J. Math. — 2014. — V. 35, No 4. — P. 333−338.
2013
1. Faizrahmanov M.Kh. Complements for Enumeration Π-0−1-degrees. Sib. Math. J. — 2013. — V. 54, No 6. — P. 1388−1395.
2012
1. Faizrahmanov M.Kh., Kalimullin I.Sh. Turing and Enumeration Jumps in the Ershov Hierarchy. J. Log. Comput. — 2012. — V. 22, No 4. — P. 737−743.
2. Kalimullin I.Sh., Faizrakhmanov M.Kh. Limitwise Monotonic Spectra of Σ-0−2-sets. Uchen. Zapiski Kazan. Univ.. Seriya Fiz.-Mat. Nauki. — 2012. — V. 154. No 2. — P. 107−116.
2011
1. Faizrakhmanov M.Kh. Turing Jumps in the Ershov Hierarchy. Algebra Logika. — 2011. — V. 50, No 3. — P. 399−414.
2. Faizrakhmanov M.Kh. A Semilattice Generated by Superlow Computably Enumerable Degrees. Russian Math. — 2011. No 1. — P. 85−90.
2010
1. Faizrahmanov M.Kh. Computable Numberings of Families of Low Sets and Turing Jumps in the Ershov Hierarchy. — 2010. Sib. Math. J. — V. 51, No 6. — P. 1435−1439.
2. Faizrakhmanov M.Kh. Decomposability of Low 2-computably Enumerable Degrees and Turing Jumps in the Ershov Hierarchy. Russian Math. — 2010. — No 12. — P. 58−66.
Contacts
Russia, 420008, Kazan, 35 Kremlievskaia st., Office 703
Phone: +7 (843) 292-72-79
Email: marat.faizrahmanov@gmail.com
Russia, 420008, Kazan, 35 Kremlievskaia st., Office 703
Phone: +7 (843) 292-72-79
Email: marat.faizrahmanov@gmail.com
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