Pro-definability of spaces of definable types
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- by Pablo Cubides Kovacsics and Jinhe Ye HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 8 (2021), 173-188
Abstract:
We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued fields and closed ordered differential fields. Furthermore, we prove pro-definability of other distinguished subspaces, some of which have an interesting geometric interpretation.
Our general strategy consists of showing that definable types are uniformly definable, a property which implies pro-definability using an argument due to E. Hrushovski and F. Loeser. Uniform definability of definable types is finally achieved by studying classes of stably embedded pairs.
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Additional Information
- Pablo Cubides Kovacsics
- Affiliation: Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
- MR Author ID: 1099792
- ORCID: 0000-0002-9689-2132
- Jinhe Ye
- Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université - Campus Pierre et Marie Curie 4, place Jussieu - Boite Courrier 247 75252 Paris Cedex 05
- MR Author ID: 1404098
- ORCID: 0000-0002-9530-8010
- Email: jinhe.ye@imj-prg.fr
- Received by editor(s): June 3, 2020
- Received by editor(s) in revised form: November 23, 2020, and February 8, 2021
- Published electronically: June 9, 2021
- Additional Notes: The first author was partially supported by the ERC project TOSSIBERG (Grant Agreement 637027), ERC project MOTMELSUM (Grant agreement 615722) and individual research grant Archimedische und nicht-archimedische Stratifizierungen höherer Ordnung, funded by the DFG. The second author was partially supported by NSF research grant DMS1500671
- Communicated by: Heike Mildenberger
- © Copyright 2021 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 8 (2021), 173-188
- MSC (2020): Primary 11S80; Secondary 11U09
- DOI: https://doi.org/10.1090/bproc/85
- MathSciNet review: 4273164