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MODEL THEORY AND COMBINATORICS OF BANNED SEQUENCES

Part of: Theory of computing Model theory

Published online by Cambridge University Press:  05 October 2020

HUNTER CHASE  and
JAMES FREITAG
HUNTER CHASE
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS CHICAGO CHICAGO, IL, USA E-mail: freitagj@gmail.com
JAMES FREITAG
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF MARYLAND, COLLEGE PARK COLLEGE PARK, MD, USA E-mail: hschase@umd.edu
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Abstract

We set up a general context in which one can prove Sauer–Shelah type lemmas. We apply our general results to answer a question of Bhaskar [1] and give a slight improvement to a result of Malliaris and Terry [7]. We also prove a new Sauer–Shelah type lemma in the context of $ \operatorname {\textrm{op}}$ -rank, a notion of Guingona and Hill [4].

Keywords

VC-dimensionLittlestone dimensionstabilityNIPonline learningquery learningPAC learning

MSC classification

Primary: 03C45: Classification theory, stability and related concepts 03C98: Applications of model theory
Secondary: 68Q32: Computational learning theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 87 , Issue 1 , March 2022 , pp. 1 - 20
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Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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