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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Imaginaries, invariant types and pseudo $ p$-adically closed fields


Authors: Samaria Montenegro and Silvain Rideau-Kikuchi
Journal: Trans. Amer. Math. Soc. 374 (2021), 803-828
MSC (2020): Primary 03C60; Secondary 03C45, 03C98, 12J12
DOI: https://doi.org/10.1090/tran/8052
Published electronically: November 18, 2020
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Abstract: In this paper, we give a general criterion for elimination of imaginaries using an abstract independence relation. We also study germs of definable functions at certain well-behaved invariant types. Finally we apply these results to prove the elimination of imaginaries in bounded pseudo $ p$-adically closed fields.


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Additional Information

Samaria Montenegro
Affiliation: Escuela de Matemática-CIMPA, Universidad de Costa Rica, Costa Rica
Email: samaria.montenegroguzman@ucr.ac.cr

Silvain Rideau-Kikuchi
Affiliation: CNRS, Sorbonne Université, Université Paris Diderot, Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG, F-75013, Paris, France
Email: silvain.rideau@imj-prg.fr

DOI: https://doi.org/10.1090/tran/8052
Received by editor(s): February 1, 2018
Received by editor(s) in revised form: January 16, 2019, August 29, 2019, and October 25, 2019
Published electronically: November 18, 2020
Additional Notes: This research was partially supported by ValCoMo (ANR-13-BS01-0006)
Article copyright: © Copyright 2020 American Mathematical Society