Fragments of arithmetic

Annals of Pure and Applied Logic 28 (1):33-71 (1985)
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We establish by elementary proof-theoretic means the conservativeness of two subsystems of analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman [6], the other is a strengthened version of a theory of Minc [14]; each has been shown to be of considerable interest for both mathematical practice and metamathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems. The results are generalized to relate a hierarchy of subsystems, all contained in the theory of arithmetic properties, to a corresponding hierarchy of fragments of arithmetic. The proof theoretic tools employed there are used to re-establish in a uniform, elementary way relationships between various fragments of arithmetic due to Parsons, Paris and Kirby, and Friedman



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Wilfried Sieg
Carnegie Mellon University

Citations of this work

Hilbert’s Program.Richard Zach - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
Partial realizations of Hilbert's program.Stephen G. Simpson - 1988 - Journal of Symbolic Logic 53 (2):349-363.

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On n-quantifier induction.Charles Parsons - 1972 - Journal of Symbolic Logic 37 (3):466-482.

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