Predicative Logic and Formal Arithmetic

Abstract
After a summary of earlier work it is shown that elementary or Kalmar arithmetic can be interpreted within the system of Russell's Principia Mathematica with the axiom of infinity but without the axiom of reducibility
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DOI 10.1305/ndjfl/1039293018
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Comparing Peano Arithmetic, Basic Law V, and Hume's Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.
Ramified Frege Arithmetic.Richard Heck - 2011 - Journal of Philosophical Logic 40 (6):715-735.

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