Regular Ultrafilters and Long Ultrapowers
Murray A. Jorgensen · Canadian Mathematical Bulletin · 1975
The Ultrapower construction, which builds a new structure AI/D from a relational structure A and an ultrafilter D on a set I, is by now a familiar tool in Model Theory and many other branches of mathematics. In this note we present a result that belongs in the theory of ordered sets, i.e. where the relational structure A has just a single binary relation <, which satisfies the axioms for a strict linear order. We assume that the reader is familiar with the definition and standard notation for ultrapowers, as may be found, for example, in [1]. We differ from [1] only in our eschewing of Gothic capitals.