Some reasons to regard the cumulative hierarchy of sets as potential rather than actual are discussed. Motivated by this, a modal set theory is developed which encapsulates this potentialist conception. The resulting theory is equi-interpretable with Zermelo Fraenkel set theory but sheds new light on the set-theoretic paradoxes and the foundations of set theory.
|Number of pages||24|
|Journal||Review of Symbolic Logic|
|Early online date||14 Mar 2013|
|Publication status||Published - Jun 2013|