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. We restate Frege’s definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege’s own indications is possible at all.
Biccuni, F., & Panza, M. (2022). Frege’s Theory of Real Numbers: A Consistent Rendering. The Review of Symbolic Logic, 15(3), 624-667. https://doi.org/10.1017/S175502032000026X