A multiverse perspective on the axiom of constructiblity
Abstract
I shall argue that the commonly held V not equal L via maximize position, which rejects the axiom of constructibility V = L on the basis that it is restrictive, implicitly takes a stand in the pluralist debate in the philosophy of set theory by presuming an absolute background concept of ordinal. The argument appears to lose its force, in contrast, on an upwardly extensible concept of set, in light of the various facts showing that models of set theory generally have extensions to models of V = L inside larger set-theoretic universes.
Keywords
Cite
@article{arxiv.1210.6541,
title = {A multiverse perspective on the axiom of constructiblity},
author = {Joel David Hamkins},
journal= {arXiv preprint arXiv:1210.6541},
year = {2012}
}
Comments
21 pages. This article expands on an argument that I made during my talk at the Asian Initiative for Infinity: Workshop on Infinity and Truth, held July 25--29, 2011 at the Institute for Mathematical Sciences, National University of Singapore. Commentary concerning this paper can be made at http://jdh.hamkins.org/multiverse-perspective-on-constructibility