Set existence principles and closure conditions: unravelling the standard view of reverse mathematics
Philosophia Mathematica 27 (2):153-176 (2019)
Abstract
It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on the powerset of the natural numbers.Author's Profile
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2018
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10.1093/philmat/nky010
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Citations of this work
Review of John Stillwell, Reverse Mathematics: Proofs from the Inside Out. [REVIEW]Benedict Eastaugh - 2020 - Philosophia Mathematica 28 (1):108-116.
Does Choice Really Imply Excluded Middle? Part II: Historical, Philosophical, and Foundational Reflections on the Goodman–Myhill Result†.Neil Tennant - 2021 - Philosophia Mathematica 29 (1):28-63.
References found in this work
Partial realizations of Hilbert's program.Stephen G. Simpson - 1988 - Journal of Symbolic Logic 53 (2):349-363.
Open questions in reverse mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Factorization of polynomials and °1 induction.S. G. Simpson - 1986 - Annals of Pure and Applied Logic 31:289.
