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August 2022 On VC-Density in VC-Minimal Theories
Vincent Guingona
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Notre Dame J. Formal Logic 63(3): 395-413 (August 2022). DOI: 10.1215/00294527-2022-0019

Abstract

We show that any formula with two free variables in a Vapnik–Chervonenkis (VC) minimal theory has VC-codensity at most 2. Modifying the argument slightly, we give a new proof of the fact that, in a VC-minimal theory where acleq=dcleq, the VC-codensity of a formula is at most the number of free variables (from the work of Aschenbrenner et al., the author, and Laskowski).

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Vincent Guingona. "On VC-Density in VC-Minimal Theories." Notre Dame J. Formal Logic 63 (3) 395 - 413, August 2022. https://doi.org/10.1215/00294527-2022-0019

Information

Received: 27 February 2021; Accepted: 27 April 2022; Published: August 2022
First available in Project Euclid: 25 September 2022

Digital Object Identifier: 10.1215/00294527-2022-0019

Subjects:
Primary: 03C45

Keywords: NIP , VC-density , VC-dimension , VC-minimal

Rights: Copyright © 2022 University of Notre Dame

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Vol.63 • No. 3 • August 2022
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