The Journal of Philosophy

Volume 111, Issue 8, August 2014

Kai Hauser, W. Hugh Woodin
Pages 397-419

Strong Axioms of Infinity and the Debate About Realism

One of the most distinctive and intriguing developments of modern set theory has been the realization that, despite widely divergent incentives for strengthening the standard axioms, there is essentially only one way of ascending the higher reaches of infinity. To the mathematical realist the unexpected convergence suggests that all these axiomatic extensions describe different aspects of the same underlying reality.