# Predicative fragments of Frege Arithmetic

```@article{Linnebo2004PredicativeFO,
title={Predicative fragments of Frege Arithmetic},
author={{\O}ystein Linnebo},
journal={Bull. Symb. Log.},
year={2004},
volume={10},
pages={153-174}
}```
Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic… Expand
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