A Remark on a Theorem of Erdos

2017/11/29 by James H. Schmerl, Schmerl, James H.
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.1711.11061

arxiv created 2017/11/29 · arxiv updated 2017/12/01

Abstract

A theorem of Erdos asserts that every infinite subset of Euclidean n-space Rⁿ has a subset of the same cardinality having no repeated distances. This theorem is generalized here as follows: If (Rⁿ,E) is an algebraic hypergraph that does not have an infinite, complete subset, then every infinite subset of it has an independent subset of the same cardinality.

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