Journal article

Free independence is not definable

Abstract:: Free independence is an important tool for studying the structure of operator algebras. It is natural to ask from the model-theoretic standpoint whether free independence is captured well in first-order model theory via the notion of a definable set. We prove that pairs of freely independent elements do not form a definable set in the sense of continuous model theory, relative to the theory of both C∗ -probability spaces and tracial von Neumann algebras.

Publication status:: Accepted

Peer review status:: Peer reviewed

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APA Style

Boulanger, W., Curda, J., Harvey, E., Li, Y., & Pi, J. (2026). Free independence is not definable. Involve.

MLA Style

Boulanger, W, et al. “Free Independence Is Not Definable.” Involve, 2026.

Chicago Style

Boulanger, W, J Curda, E Harvey, Y Li, and J Pi. 2026. “Free Independence Is Not Definable.” Involve.
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Authors

+ Boulanger, W More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author
ORCID:: 0009-0007-4947-5831

+ Curda, J More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author
ORCID:: 0000-0002-5168-6095

+ Harvey, E More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Computer Science
Role:: Author

+ Li, Y More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Pi, J More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author
ORCID:: 0000-0003-1256-1086

+ Engineering and Physical Sciences Research Council More from this funder

Funder identifier:: https://ror.org/0439y7842
Grant:: EP/X026647/1

Publisher:: Mathematical Sciences Publishers (MSP)
Journal:: Involve More from this journal
Acceptance date:: 2026-02-16
EISSN:: 1944-4184
ISSN:: 1944-4176

Language:: English
Pubs id:: 2413313
Local pid:: pubs:2413313
Deposit date:: 2026-05-01
ARK identifier:: ark:/29072/ora_96aa33222d76442493f7f82e46eaa033

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