Volume 111, Issue 8, August 2014
Kai Hauser, W. Hugh Woodin
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.