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September 2020 Definable Functions and Stratifications in Power-Bounded T -Convex Fields
Erick García Ramírez
Notre Dame J. Formal Logic 61(3): 441-465 (September 2020). DOI: 10.1215/00294527-2020-0013

Abstract

We study properties of definable sets and functions in power-bounded T -convex fields, proving that the latter have the multidimensional Jacobian property and that the theory of T -convex fields is b -minimal with centers. Through these results and work of I. Halupczok we ensure that a certain kind of geometrical stratifications exist for definable objects in said fields. We then discuss a number of applications of those stratifications, including applications to Archimedean o-minimal geometry.

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Erick García Ramírez. "Definable Functions and Stratifications in Power-Bounded T -Convex Fields." Notre Dame J. Formal Logic 61 (3) 441 - 465, September 2020. https://doi.org/10.1215/00294527-2020-0013

Information

Received: 21 November 2017; Accepted: 17 December 2019; Published: September 2020
First available in Project Euclid: 9 September 2020

MathSciNet: MR4159165
Digital Object Identifier: 10.1215/00294527-2020-0013

Subjects:
Primary: 03C98
Secondary: 03C64, 14P10

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 3 • September 2020
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