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. In: Philosophia Mathematica: pp. 1-24

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 math- ematics, and argue that they are best understood as closure conditions on the powerset of the natural numbers.

• Item Type: Journal article
• Form of publication: Postprint
• Keywords: reverse mathematics; foundations of mathematics
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP)
• Subjects: 100 Philosophy and Psychology > 160 Logic
• ISSN: 0031-8019
• Language: English