6 research outputs found
The logic of the reverse mathematics zoo
Building on previous work by Mummert, Saadaoui and Sovine,
we study the logic underlying the web of implications and nonimplications
which constitute the so called reverse mathematics zoo. We introduce a
tableaux system for this logic and natural deduction systems for important
fragments of the language
Set existence principles and closure conditions: unravelling the standard view of reverse mathematics
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