Nonstandard methods for upper Banach density problems.

DOI10.1006/jnth.2001.2671zbMath1071.11503OpenAlexW2054061997MaRDI QIDQ1612521

Renling Jin

Publication date: 25 August 2002

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/11b694db5c60e9c3786d276c6f013dec9c1763c7

Mathematics Subject Classification ID

Density, gaps, topology (11B05) Simultaneous homogeneous approximation, linear forms (11J13) Nonstandard models in mathematics (03H05) Nonstandard arithmetic (number-theoretic aspects) (11U10)

Related Items (13)

Stability and sparsity in sets of natural numbers ⋮ Kneser's theorem for upper Banach density ⋮ Freiman's inverse problem with small doubling property ⋮ Inverse problem for cuts ⋮ Assouad dimensions of Moran sets and Cantor-like sets ⋮ The sumset phenomenon ⋮ Characterizing the structure of \(A+B\) when \(A+B\) has small upper Banach density ⋮ A note on uniform or Banach density ⋮ A combinatorial proof of the dense Hindman's theorem ⋮ Near arithmetic progressions in sparse sets ⋮ Plünnecke’s Theorem for asymptotic densities ⋮ Solution to the inverse problem for upper asymptotic density ⋮ Inverse problem for upper asymptotic density

Cites Work

• Sequences in countable nonstandard models of the natural numbers
• Some nonstandard methods in combinatorial number theory
• Applications of Nonstandard Models and Lebesgue Measure to Sequences of Natural Numbers
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