Geodesic
Regular Ultrafilters and Long Ultrapowers
Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 41-43

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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. 
Jorgensen, Murray. Regular Ultrafilters and Long Ultrapowers. Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 41-43. doi: 10.4153/CMB-1975-008-x
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     title = {Regular {Ultrafilters} and {Long} {Ultrapowers}},
     journal = {Canadian mathematical bulletin},
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     year = {1975},
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     number = {1},
     doi = {10.4153/CMB-1975-008-x},
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