An o-minimal Szemerédi-Trotter theorem

Saugata Basu*, Orit E. Raz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We prove an analog of the Szemerédi-Trotter Theorem in the plane for definable curves and points in any o-minimal structure over an arbitrary real closed field R. One new ingredient in the proof is an extension of the well known crossing number inequality for graphs to the case of embeddings in any o-minimal structure over an arbitrary real closed field.

Original languageAmerican English
Pages (from-to)223-239
Number of pages17
JournalQuarterly Journal of Mathematics
Volume69
Issue number1
DOIs
StatePublished - 1 Mar 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017. Published by Oxford University Press. All rights reserved.

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