Cruz-Filipe, L.Ferreira, Fernando2024-09-112024-09-112015Luís Cruz-Filipe. Fernando Ferreira. "The Finitistic Consistency of Heck’s Predicative Fregean System." Notre Dame J. Formal Logic 56 (1) 61 - 79, 2015. https://doi.org/10.1215/00294527-2835110http://hdl.handle.net/10400.26/52045Frege’s theory is inconsistent (Russell’s paradox). However, the predicative version of Frege’s system is consistent. This was proved by Richard Heck in 1996 using a model-theoretic argument. In this paper, we give a finitistic proof of this consistency result. As a consequence, Heck’s predicative theory is rather weak (as was suspected).engconsistencyFregean arithmeticstrict predicativityjournal articlehttps://doi.org/10.1215/00294527-2835110