Ashutosh Kumar: Avoiding rational distances

Infinite Combinatorics Seminar (BIU)

16/November/2014, 10:15-12:00,
Room 201, Building 216, Bar-Ilan University

Speaker: Ashutosh Kumar (HUJI)

Title: Avoiding rational distances

Abstract: Komjath has asked the following question: Let X be a subset of Euclidean space. Must there exist a subset Y of X such that X and Y have same outer measure and the distance between any two points in Y is irrational?

We’ll show that this is true in dimension one. Our proof relies on some work of Gitik and Shelah on forcings with sigma ideals.

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