Density Problems and Freiman’s Inverse Problems

Renling Jin ()
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Renling Jin: College of Charleston, Department of Mathematics

Chapter Chapter 10 in Nonstandard Analysis for the Working Mathematician, 2015, pp 403-441 from Springer

Abstract: 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.

Keywords: Hyperfinite Set; Saturating Counter; Nonstandard Analysis; Combinatorial Number Theory; Transfer Principle (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-7327-0_10

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DOI: 10.1007/978-94-017-7327-0_10

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