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Density Problems and Freiman’s Inverse Problems

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Nonstandard Analysis for the Working Mathematician

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Abstract

In this chapter we present applications of nonstandard analysis to density problems and Freiman’s inverse problems in combinatorial number theory. The reader is assumed to be familiar with some basic knowledge and principles in nonstandard analysis such as nonstandard extensions of the standard universe, transfer principle, standard part map, distinctions among standard, internal, and external sets and arguments, hyperfinite sets, hyperfinite integers, overspill/underspill principle, countable saturation, etc.

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Authors and Affiliations

  1. Department of Mathematics, College of Charleston, Charleston, SC, 29424, USA

    Renling Jin

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  1. Renling Jin
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Correspondence to Renling Jin .

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Editors and Affiliations

  1. Department of Mathematics, University of Illinois, Urbana, Illinois, USA

    Peter A. Loeb

  2. Mathematical Institute, University of Tübingen, Tübingen, Germany

    Manfred P. H. Wolff

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Jin, R. (2015). Density Problems and Freiman’s Inverse Problems. In: Loeb, P., Wolff, M. (eds) Nonstandard Analysis for the Working Mathematician. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7327-0_10

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