Approximation Theory and Elementary Submodels

TL;DR

This paper employs set-theoretic elementary submodel techniques to provide new, concise proofs of established theorems in approximation theory, often achieving stronger results.

Contribution

It introduces the use of elementary submodel arguments in approximation theory to simplify proofs and enhance existing theorems.

Findings

Shorter proofs of classical theorems

Stronger results in approximation theory

Novel application of set-theoretic methods

Abstract

\emph{Approximation Theory} uses nicely-behaved subcategories to understand entire categories, just as projective modules are used to approximate arbitrary modules in classical homological algebra. We use set-theoretic \emph{elementary submodel arguments} to give new, short proofs of well-known theorems in approximation theory, sometimes with stronger results.