Set existence principles and closure conditions: unravelling the standard view of reverse mathematics

Philosophia Mathematica 27 (2):153-176 (2019)
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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.

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Benedict Eastaugh
Ludwig Maximilians Universität, München

References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Systems of predicative analysis.Solomon Feferman - 1964 - Journal of Symbolic Logic 29 (1):1-30.
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.

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