FUNDAMENTAL THEOREMS OF ANALYSIS IN FORMALLY REAL FIELDS
Angelina Ilić Stepić, Žarko Mijajlović · 2008
Abstract. 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? AMS Mathematics Subject Classification (2000): 12D15, 12L12. Key words and phrases: formally real field,real closed field, submodel complete, fundamental theorems of analysis. 1.