An o-minimal Szemerédi-Trotter theorem

2016/11/22 by Basu, Saugata, Raz, Orit E.
#03C64 #05D40 #Combinatorics (math.CO) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1611.07362

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.

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