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The prehistory of the subsystems of second-order arithmetic
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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. ISSN 1755-0203.
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Official URL: https://doi.org/10.1017/S1755020316000411
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 | ||||||||
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Subjects: | B Philosophy. Psychology. Religion > BC Logic Q Science > QA Mathematics |
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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: |
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Volume: | 10 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 357-396 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 21 December 2016 |
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