Frege's Theory of Real Numbers: A Consistent Rendering

Frege’s definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege’s ill-fated Basic Law V. Werestate Frege’s definition in a consistent logical framework and investigate whether it canprovide a logical foundation of real analysis. Our conclusion will deem it doubtful that sucha foundation along the lines of Frege’s own indications is possible at all.