PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Separation for isometric group actions and hyperimaginary independence

Volume 259 / 2022

Gabriel Conant, James Hanson Fundamenta Mathematicae 259 (2022), 97-109 MSC: Primary 03C66; Secondary 20B99. DOI: 10.4064/fm167-2-2022 Published online: 26 May 2022


We generalize P. M. Neumann’s Lemma to the setting of isometric actions on metric spaces and use it to prove several results in continuous model theory related to algebraic independence. In particular, we show that algebraic independence satisfies the full existence axiom (which answers a question of Goldbring) and is implied by dividing independence. We also use the relationship between hyperimaginaries and continuous imaginaries to derive further results that are new even for discrete theories. Specifically, we show that if $\mathbb M$ is a monster model of a discrete or continuous theory, then bounded-closure independence in $\mathbb M^{{\rm heq}}$ satisfies full existence (which answers a question of Adler) and is implied by dividing independence.


  • Gabriel ConantDepartment of Mathematics
    The Ohio State University
    Columbus, OH 43210, USA
  • James HansonDepartment of Mathematics
    University of Maryland
    College Park, MD 20742, USA

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image