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- Title
THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC.
- Authors
DEAN, WALTER; WALSH, SEAN
- 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.
- Subjects
REVERSE mathematics; TRANSFINITE numbers; DESCRIPTIVE set theory; DEFINABILITY theory (Mathematical logic); POINCARE conjecture
- Publication
Review of Symbolic Logic, 2017, Vol 10, Issue 2, p357
- ISSN
1755-0203
- Publication type
Article
- DOI
10.1017/S1755020316000411