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

Eastaugh, Benedict (2018) Set existence principles and closure conditions: unravelling the standard view of reverse mathematics. [Preprint]

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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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Item Type: Preprint
Creators:
CreatorsEmailORCID
Eastaugh, Benedict0000-0002-6629-3032
Keywords: reverse mathematics, foundations of mathematics
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Proof
Specific Sciences > Mathematics
Depositing User: Benedict Eastaugh
Date Deposited: 18 Feb 2018 14:24
Last Modified: 18 Feb 2018 14:24
Item ID: 14393
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Proof
Specific Sciences > Mathematics
Date: 16 February 2018
URI: http://philsci-archive.pitt.edu/id/eprint/14393

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