Alexander Berenstein
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Alexander Berenstein has a total of 59 co-authors. Here are the top co-authors by number of shared publications:
Itaï Ben Yaacov
Universite Claude Bernard — Lyon 1
6 shared publications- Evgueni Vassiliev
Grenfell Campus, Memorial University of Newfoundland, Corner Brook, Canada
5 shared publications C. Ward Henson
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN, 1409 WEST GREEN STREET, URBANA, ILLINOIS 61801, USAhttp://www.math.uiuc.edu/∼henson
4 shared publications- Anton Setzer
Swansea University
3 shared publications - Damir D. Dzhafarov
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
3 shared publications - Hiroshi Sakai
Graduate School of System Informatics, Kobe University, Kobe, Japan
3 shared publications
Latest Publications
- Open Access
- 16 October 2026
- Published by Cambridge University Press (CUP) in The Bulletin of Symbolic Logic
- p. 1-36
MODEL THEORY OF HILBERT SPACES EXPANDED BY NORMAL OPERATORS
We study expansions of Hilbert spaces with a bounded normal operator T . We axiomatize this theory in a natural language and identify all of its completions. We prove the definability of the adjoint $T^*$ upper T Superscript asterisk and prove quantifier elimination for every completion after adding $T^*$ upper T Superscript asterisk to the language. We identify types with measures on the spectrum of the operator and show that the logic topology on the type space corresponds to the weak*-topology on the space of measures. We also give a precise formula for the metric on the space of $1$ 1 -types. We prove all completions are stable and characterize the stability spectrum of the theory in terms of the spectrum of the operator. We also show all completions, regardless of their spectrum, are $\omega $ omega -stable up to perturbations.- 16 October 2026
- Published by Cambridge University Press (CUP) in The Bulletin of Symbolic Logic
- p. 1-36
Open AccessMODEL THEORY OF HILBERT SPACES EXPANDED BY NORMAL OPERATORS
We study expansions of Hilbert spaces with a bounded normal operator T . We axiomatize this theory in a natural language and identify all of its completions. We prove the definability of the adjoint $T^*$ upper T Superscript asterisk and prove quantifier elimination for every completion after adding $T^*$ upper T Superscript asterisk to the language. We identify types with measures on the spectrum of the operator and show that the logic topology on the type space corresponds to the weak*-topology on the space of measures. We also give a precise formula for the metric on the space of $1$ 1 -types. We prove all completions are stable and characterize the stability spectrum of the theory in terms of the spectrum of the operator. We also show all completions, regardless of their spectrum, are $\omega $ omega -stable up to perturbations. - Open Access
- 6 February 2026
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 90 (4) , f1-f3
JSL volume 90 issue 4 Cover and Front matter
- 6 February 2026
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 90 (4) , f1-f3
Open AccessJSL volume 90 issue 4 Cover and Front matter
- 18 March 2025
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 90 (1) , 68-104
DIMENSION AND MEASURE IN PSEUDOFINITE H-STRUCTURES
We study H-structures associated with $SU$ -rank 1 measurable structures. We prove that the $SU$ -rank of the expansion is continuous and that it is uniformly definable in terms of the parameters of the formulas. We also introduce notions of dimension and measure for definable sets in the expansion and prove they are uniformly definable in terms of the parameters of the formulas.- 18 March 2025
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 90 (1) , 68-104
DIMENSION AND MEASURE IN PSEUDOFINITE H-STRUCTURES
We study H-structures associated with $SU$ -rank 1 measurable structures. We prove that the $SU$ -rank of the expansion is continuous and that it is uniformly definable in terms of the parameters of the formulas. We also introduce notions of dimension and measure for definable sets in the expansion and prove they are uniformly definable in terms of the parameters of the formulas.- Open Access
- 21 February 2023
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 88 (1) , f1-f3
JSL volume 88 issue 1 Cover and Front matter
Manuscripts should be submitted using EditFlow at https://ef.msp.org/submit/asl_jsl, where instructions directed specifi cally at using the system can also be found. Authors should keep a complete copy of their submission and all electronic fi les from which it was created. They should also consult the more general guidelines for the submission of manuscripts at https://aslonline.org/journals/the-journal-of-symbolic-logic/submission-guidelines/. These instructions include the Association's standards about previous publication and plagiarism as well as information about copyrights and electronic copies of published papers. No print off prints will be supplied but authors will receive a link to a freely accessible electronic pdf of their published article. Print off prints may be purchased if required.
- 21 February 2023
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 88 (1) , f1-f3
Open AccessJSL volume 88 issue 1 Cover and Front matter
Manuscripts should be submitted using EditFlow at https://ef.msp.org/submit/asl_jsl, where instructions directed specifi cally at using the system can also be found. Authors should keep a complete copy of their submission and all electronic fi les from which it was created. They should also consult the more general guidelines for the submission of manuscripts at https://aslonline.org/journals/the-journal-of-symbolic-logic/submission-guidelines/. These instructions include the Association's standards about previous publication and plagiarism as well as information about copyrights and electronic copies of published papers. No print off prints will be supplied but authors will receive a link to a freely accessible electronic pdf of their published article. Print off prints may be purchased if required.
- Open Access
- 17 November 2022
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 87 (4) , f1-f3
JSL volume 87 issue 4 Cover and Front matter
Manuscripts should be submitted using EditFlow at https://ef.msp.org/submit/asl_jsl, where instructions directed specifi cally at using the system can also be found. Authors should keep a complete copy of their submission and all electronic fi les from which it was created. They should also consult the more general guidelines for the submission of manuscripts at https://aslonline.org/journals/the-journal-of-symbolic-logic/submission-guidelines/. These instructions include the Association's standards about previous publication and plagiarism as well as information about copyrights and electronic copies of published papers. No print offprints will be supplied but authors will receive a link to a freely accessible electronic pdf of their published article. Print offprints may be purchased if required.
- 17 November 2022
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 87 (4) , f1-f3
Open AccessJSL volume 87 issue 4 Cover and Front matter
Manuscripts should be submitted using EditFlow at https://ef.msp.org/submit/asl_jsl, where instructions directed specifi cally at using the system can also be found. Authors should keep a complete copy of their submission and all electronic fi les from which it was created. They should also consult the more general guidelines for the submission of manuscripts at https://aslonline.org/journals/the-journal-of-symbolic-logic/submission-guidelines/. These instructions include the Association's standards about previous publication and plagiarism as well as information about copyrights and electronic copies of published papers. No print offprints will be supplied but authors will receive a link to a freely accessible electronic pdf of their published article. Print offprints may be purchased if required.
- 8 October 2021
- Published by Springer Nature in Archive for Mathematical Logic
- Vol. 61 (3-4) , 345-372
Definable groups in dense pairs of geometric structures
- 8 October 2021
- Published by Springer Nature in Archive for Mathematical Logic
- Vol. 61 (3-4) , 345-372
Definable groups in dense pairs of geometric structures
- 5 May 2021
- Published by Springer Nature in Archive for Mathematical Logic
- Vol. 60 (7-8) , 1019-1041
Definable connectedness of randomizations of groups
- 5 May 2021
- Published by Springer Nature in Archive for Mathematical Logic
- Vol. 60 (7-8) , 1019-1041
Definable connectedness of randomizations of groups
- 5 July 2019
- Published by Springer Nature in Archive for Mathematical Logic
- Vol. 59 (1-2) , 197-228
Fields with a dense-codense linearly independent multiplicative subgroup
- 5 July 2019
- Published by Springer Nature in Archive for Mathematical Logic
- Vol. 59 (1-2) , 197-228
Fields with a dense-codense linearly independent multiplicative subgroup
- 27 December 2017
- Published by Wiley in Mathematical Logic Quarterly
- Vol. 63 (6) , 552-573
Supersimple structures with a dense independent subset
- 27 December 2017
- Published by Wiley in Mathematical Logic Quarterly
- Vol. 63 (6) , 552-573
Supersimple structures with a dense independent subset
- 19 January 2016
- Published by Wiley in Mathematical Logic Quarterly
- Vol. 62 (1-2) , 16-24
Dense codense predicates and the NTP2
- 19 January 2016
- Published by Wiley in Mathematical Logic Quarterly
- Vol. 62 (1-2) , 16-24
Dense codense predicates and the NTP2