On uniform definability of types over finite sets for NIP formulas

Shlomo Eshel; Itay Kaplan

doi:10.1142/S021906132150015X

On uniform definability of types over finite sets for NIP formulas

Shlomo Eshel, Itay Kaplan^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Combining two results from machine learning theory we prove that a formula is NIP if and only if it satisfies uniform definability of types over finite sets (UDTFS). This settles a conjecture of Laskowski.

Original language	American English
Article number	2150015
Pages (from-to)	2150015:1-2150015:13
Number of pages	13
Journal	Journal of Mathematical Logic
Volume	21
Issue number	3
DOIs	https://doi.org/10.1142/S021906132150015X
State	Published - 1 Dec 2021

Bibliographical note

Funding Information:
I. Kaplan would like to thank the Israel Science Foundation for partial support of this research (Grants Nos. 1533/14 and 1254/18). We thank the anonymous referee for their remarks, and specifically for suggesting to add Remark 12 which certainly helps the presentation.

Publisher Copyright:
© 2021 World Scientific Publishing Company.

Keywords

Local UDTFS
local NIP
recursive teaching dimension
sample compression schemes

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10.1142/S021906132150015X

Cite this

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KW - sample compression schemes

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On uniform definability of types over finite sets for NIP formulas

Abstract

Bibliographical note

Keywords

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