Marat Faizrahmanov
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, Computable Model Theory, Admissible Sets
Orcid ID: 0000-0002-4519-9696
Researcher ID: K-7976-2015
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, Computable Model Theory, Admissible Sets
Orcid ID: 0000-0002-4519-9696
Researcher ID: K-7976-2015
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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 «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 p.
[2] Fixed Point Theorems for Minimal Numberings. Journal of Logic and Computation. 35:2 (2025), exad074. 15 p.
[3] A Family Whose Computable Numberings are All Complete. Journal of Logic, Language and Information. 34:1 (2025), 23-35.
[4] Computable Operators on Left-c.e. Reals and Their Continuity Properties. Logic Journal of the IGPL. 33:3 (2025), jzaf011. 11 p.
[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 p.
[2] Fixed Point Theorems for Minimal Numberings. Journal of Logic and Computation. 35:2 (2025), exad074. 15 p.
[3] A Family Whose Computable Numberings are All Complete. Journal of Logic, Language and Information. 34:1 (2025), 23-35.
[4] Computable Operators on Left-c.e. Reals and Their Continuity Properties. Logic Journal of the IGPL. 33:3 (2025), jzaf011. 11 p.
[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 p.
[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. Art. No 2250218 (2022).
[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. Art. No 2250218 (2022).
[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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