## Stable decompositions and rigidity for products of countable equivalence relations

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- by Pieter Spaas PDF
- Trans. Amer. Math. Soc.
**376**(2023), 1867-1894 Request permission

## Abstract:

We show that the “stabilization” of any countable ergodic probability measure preserving (p.m.p.) equivalence relation which is not Schmidt, i.e. admits no central sequences in its full group, always gives rise to a stable equivalence relation with a unique stable decomposition, providing the first non-strongly ergodic such examples. In the proof, we moreover establish a new local characterization of the Schmidt property. We also prove some new structural results for product equivalence relations and orbit equivalence relations of diagonal product actions.## References

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## Additional Information

**Pieter Spaas**- Affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
- MR Author ID: 1272392
- Email: pisp@math.ku.dk
- Received by editor(s): May 8, 2021
- Received by editor(s) in revised form: November 7, 2021, and August 17, 2022
- Published electronically: December 15, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**376**(2023), 1867-1894 - MSC (2020): Primary 37A20, 46L10; Secondary 03E15
- DOI: https://doi.org/10.1090/tran/8800
- MathSciNet review: 4549694