Fundamental theorems of analysis in formally real fields. (English) Zbl 1224.12012

Ilić Stepić, Angelina; Mijajlović, Žarko

Novi Sad J. Math. 38, No. 3, 27-32 (2008).

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?

Reviewer: Dragan Blagojević (Beograd)

MSC:

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.)

Keywords:

formally real field; real closed field; elimination of quantifiers; fundamental theorem of analysis