Almost all sets of nonnegative integers and their small perturbations are not sumsets

DOI10.1090/proc/16392zbMath1526.11004arXiv2212.13852OpenAlexW4313591981MaRDI QIDQ6106037

Paolo Leonetti

Publication date: 27 June 2023

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.13852

zbMATH Keywords

sumsetmeager setirreducible settotally irreducible set

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Density, gaps, topology (11B05) Additive bases, including sumsets (11B13) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

• Generalized kinds of density and the associated ideals
• Additive decomposability of multiplicatively defined sets
• A proof of a sumset conjecture of Erdős
• Erdős-Ulam ideals vs. simple density ideals
• An additive problem for powers of primes
• Tauberian theorems for ordinary convergence
• Convergent subseries of divergent series
• Limit points of subsequences
• Properties of simple density ideals
• Ein metrischer Satz über Mengen ganzer Zahlen
• The maximum domain of attraction of multivariate extreme value distributions is small
• Additive decompositions of sets with restricted prime factors
• Über totalprimitive Folgen
• On the notions of upper and lower density
• A short proof of a conjecture of Erd\"os proved by Moreira, Richter and Robertson
• Most numbers are not normal
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