- J. D. Hamkins, “The set-theoretic multiverse,” Review of Symbolic Logic, vol. 5, pp. 416-449, 2012.
`@ARTICLE{Hamkins2012:TheSet-TheoreticalMultiverse, AUTHOR = {Joel David Hamkins}, TITLE = {The set-theoretic multiverse}, JOURNAL = {Review of Symbolic Logic}, YEAR = {2012}, volume = {5}, number = {}, pages = {416--449}, month = {}, note = {}, url = {http://jdh.hamkins.org/themultiverse}, doi = {10.1017/S1755020311000359}, abstract = {}, keywords = {}, source = {}, eprint = {1108.4223}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous diversity of set-theoretic possibilities, a phenomenon that challenges the universe view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for.

Multiversive at n-Category Cafe | Multiverse on Mathoverflow