Melvyn B. Nathanson
Published 2024-01-23Version 1
Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and polynomial equations with the property that solutions for all finite subsets of the set of equations implies the existence of a solution for the infinite set of equations.
On the Number of Distinct Tilings of Finite Subsets of $\mathbb{Z}^{d}$ With Tiles of Fixed Size
Pairwise sums in colourings of the reals
Polynomial equations in function fields
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