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THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC

Published online by Cambridge University Press:  20 February 2017

WALTER DEAN
Affiliation:
Department of Philosophy, University of Warwick
SEAN WALSH
Affiliation:
Department of Logic and Philosophy of Science, University of California, Irvine
Corresponding

Abstract

This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program promoted by Friedman and Simpson. We look in particular at: (i) the long arc from Poincaré to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the lecture notes and publications of Hilbert and Bernays, (iii) the uncertainty as to the constructive status of principles equivalent to Weak König’s Lemma, and (iv) the large-scale intellectual backdrop to arithmetical transfinite recursion in descriptive set theory and its effectivization by Borel, Lusin, Addison, and others.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2017 

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