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o-minimal expansions of real closed fields and completeness in the sense of Scott

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Abstract

We consider an o-minimal expansion M=(R,<,+,...) of a real closed field, and a real closed field S, complete in the sense of D. Scott, containing R as a dense subfield. We show that M has an elementary extension N=(S,<,+,...) with domain S. Moreover, such a structure N with domain S is unique.
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Dates and versions

hal-03704341 , version 1 (24-06-2022)

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  • HAL Id : hal-03704341 , version 1

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Olivier Frécon. o-minimal expansions of real closed fields and completeness in the sense of Scott. 2015. ⟨hal-03704341⟩
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