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 | ||||||
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| 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 |
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| 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 |
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| Date: | 16 February 2018 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/14393 |
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