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On projections of the tails of a power

  • Samuel M. Corson ORCID logo EMAIL logo and Saharon Shelah
Published/Copyright: April 4, 2024

Abstract

Let 𝜅 be an inaccessible cardinal, 𝔘 a universal algebra, and the equivalence relation on U κ of eventual equality. From mild assumptions on 𝜅, we give general constructions of E End ( U κ / ) satisfying E E = E which do not descend from Δ End ( U κ ) having small strong supports. As an application, there exists an E End ( Z κ / ) which does not come from a Δ End ( Z κ ) .

MSC 2020: 20A15; 03E55; 03G05

Award Identifier / Grant number: EP/V521917/1

Funding source: Eusko Jaurlaritza

Award Identifier / Grant number: IT1483-22

Award Identifier / Grant number: PID2019-107444GA-I00

Award Identifier / Grant number: PID2020-117281GB-I00

Award Identifier / Grant number: JSF 1838/19

Award Identifier / Grant number: DMS 1833363

Funding statement: The work of the first author was supported by the Additional Funding Programme for Mathematical Sciences, delivered by EPSRC (EP/V521917/1) and the Heilbronn Institute for Mathematical Research. Also by the Basque Government Grant IT1483-22 and Spanish Government Grants PID2019-107444GA-I00 and PID2020-117281GB-I00. The work of the second author was supported by JSF 1838/19: The Israel Science Foundation (2019–2023) and Rutgers 2018 DMS 1833363: NSF DMS Rutgers visitor program (PI S. Thomas) (2018–2022). Paper number 1233 on Shelah’s archive.

Acknowledgements

The authors thank the anonymous referee for the careful reading and suggested improvements of the paper.

  1. Communicated by: Manfred Droste

References

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Received: 2022-12-08
Revised: 2024-03-04
Published Online: 2024-04-04
Published in Print: 2024-07-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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