Dean, Walter and Walsh, Sean (2017) The prehistory of the subsystems of second-order arithmetic. The Review of Symbolic Logic, 10 (2). pp. 357-396.

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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 of 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.

Item Type:	Journal Article
Subjects:	B Philosophy. Psychology. Religion > BC Logic Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Philosophy
Journal or Publication Title:	The Review of Symbolic Logic
Publisher:	Cambridge University Press
ISSN:	1755-0203
Official Date:	June 2017
Dates:	Date Event June 2017 Published 20 February 2017 Available 16 December 2016 Available
Date of first compliant deposit:	21 December 2016
Volume:	10
Number:	2
Page Range:	pp. 357-396
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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