Predicative Logic and Formal Arithmetic

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Notre Dame Journal of Formal Logic 39 (1):1-17 (1998)
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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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10.1305/ndjfl/1039293018

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John Burgess
Princeton University

Citations of this work

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 G. Heck - 2011 - Journal of Philosophical Logic 40 (6):715-735.
Type theory.Thierry Coquand - 2008 - Stanford Encyclopedia of Philosophy.
Interpretability in Robinson's Q.Fernando Ferreira & Gilda Ferreira - 2013 - Bulletin of Symbolic Logic 19 (3):289-317.
Russell's 1925 logic.A. P. Hazen & J. M. Davoren - 2000 - Australasian Journal of Philosophy 78 (4):534 – 556.

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References found in this work

Systems of predicative analysis.Solomon Feferman - 1964 - Journal of Symbolic Logic 29 (1):1-30.
On the consistency of the first-order portion of Frege's logical system.Terence Parsons - 1987 - Notre Dame Journal of Formal Logic 28 (1):161-168.
Predicative foundations of arithmetic.Solomon Feferman & Geoffrey Hellman - 1995 - Journal of Philosophical Logic 24 (1):1 - 17.
Grundgesetze der Arithmetik I §§29‒32.Richard G. Heck - 1997 - Notre Dame Journal of Formal Logic 38 (3):437-474.
A minimal predicative set theory.Franco Montagna & Antonella Mancini - 1994 - Notre Dame Journal of Formal Logic 35 (2):186-203.

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