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Fundamental theorems of analysis in formally real fields. (English) Zbl 1224.12012
Authors’ summary: The theory of real closed fields admits elimination of quantifiers, therefore fundamental theorems of analysis hold for all definable functions in all real closed fields. We consider the opposite problem: If we assume that in a formally real field some fundamental theorem of analysis holds, would the formally real field be actually real closed?
12L12 Model theory of fields
26A03 Foundations: limits and generalizations, elementary topology of the line
12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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