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Regular Ultrafilters and Long Ultrapowers

Published online by Cambridge University Press:  20 November 2018

Murray Jorgensen
Murray Jorgensen*
Affiliation:
Biometrics Section Ministry of Agriculture and Fisheries P.O. Box 1500, Wellington, New Zealand
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 41 - 43
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bell, J. L. and Slomson, A. B., Models and Ultraproducts: An Introduction. Amsterdam (1970).Google Scholar
2. Keisler, H. J., Limit Ultrapowers, Trans. Amer. Math. Soc. 107 (1963) pp. 382-408.Google Scholar
3. Kunen, K. and Prikry, K., On Descendingly Incomplete Ultrafilters, to appear.Google Scholar