Vapnik-Chervonenkis density in some theories without the independence property, I
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Abstract:
We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weakly quasi-o-minimal, and $P$-minimal theories.References
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Additional Information
- Matthias Aschenbrenner
- Affiliation: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, California 90095-1555
- Email: matthias@math.ucla.edu
- Alf Dolich
- Affiliation: Department of Mathematics and Computer Science, Kingsborough Community College (CUNY), 2001 Oriental Boulevard, Brooklyn, New York 11235
- Address at time of publication: Department of Mathematics, CUNY Graduate Center, 365 5th Avenue, New York, New York 10016
- MR Author ID: 729396
- Email: alfredo.dolich@kbcc.cuny.edu
- Deirdre Haskell
- Affiliation: Department of Mathematics and Statistics, McMaster University, 1280 Main Street W., Hamilton, Ontario L8S 4K1, Canada
- MR Author ID: 324531
- Email: haskell@math.mcmaster.ca
- Dugald Macpherson
- Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
- MR Author ID: 224239
- Email: h.d.macpherson@leeds.ac.uk
- Sergei Starchenko
- Affiliation: Department of Mathematics, University of Notre Dame, 255 Hurley Building, Notre Dame, Indiana 46556-4618
- MR Author ID: 237161
- Email: starchenko.1@nd.edu
- Received by editor(s): December 23, 2011
- Received by editor(s) in revised form: December 10, 2014
- Published electronically: December 22, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 5889-5949
- MSC (2010): Primary 03C45, 03C64
- DOI: https://doi.org/10.1090/tran/6659
- MathSciNet review: 3458402
Dedicated: For Lou van den Dries, on his 60th birthday