Strong Axioms of Infinity and the Debate About Realism

Journal of Philosophy 111 (8):397-419 (2014)
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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



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W. Hugh Woodin
Harvard University

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Why Believe Infinite Sets Exist?Andrei Mărăşoiu - 2018 - Axiomathes 28 (4):447-460.
Characterizations of ordinal analysis.James Walsh - 2023 - Annals of Pure and Applied Logic 174 (4):103230.

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