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Foundations of Analysis over Surreal Number Fields (North-Holland Mathematical Library)
Foundations of Analysis over Surreal Number Fields (North-Holland Mathematical Library)
Date: 13 April 2011, 05:46

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It is well-known that the field Ft of all real numbers is a real- closed field and that, up to isomorphism, it is the only Dedekind-complete ordered field. Artin and Schreier generalized the algebraic properties of the reals to form the rich, interesting theory or real-closed fields. Among other things, they showed that any ordered field has an algebraic extension that is real-closed, and which is uniquely determined up to isomorphism. Many interesting non-Archimedean, real-closed fields F are known. Under the interval topology, any ordered field is a topological field. Under that topology, F is not Dedekind-complete, is not locally connected, and is not locally compact.

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