Predicative Logic and Formal Arithmetic

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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Richard Heck (2011). Ramified Frege Arithmetic. Journal of Philosophical Logic 40 (6):715-735.

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Charles McCarty (2013). Paradox and Potential Infinity. Journal of Philosophical Logic 42 (1):195-219.
Richard Heck (2011). Ramified Frege Arithmetic. Journal of Philosophical Logic 40 (6):715-735.
Fernando Ferreira (2006). Comments on Predicative Logic. Journal of Philosophical Logic 35 (1):1 - 8.
Jonathan P. Seldin (1975). Arithmetic as a Study of Formal Systems. Notre Dame Journal of Formal Logic 16 (4):449-464.

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