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Some properties of regular and rational sets

Volume 182 / 2018

Konrad Deka Acta Arithmetica 182 (2018), 279-284 MSC: 11B75, 37A45. DOI: 10.4064/aa170429-14-10 Published online: 12 January 2018


We study properties of rational and regular sets of integers. The main result is that every rational set can be split into two regular ones. It follows that the union of two regular sets need not be regular. This answers a question of Bergelson and Ruzsa.


  • Konrad DekaInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland

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