Archive for History of Exact Sciences

, Volume 69, Issue 2, pp 125–151 | Cite as

How Woodin changed his mind: new thoughts on the Continuum Hypothesis

  • Colin J. RittbergEmail author


The Continuum Problem has inspired set theorists and philosophers since the days of Cantorian set theory. In the last 15 years, W. Hugh Woodin, a leading set theorist, has not only taken it upon himself to engage in this question, he has also changed his mind about the answer. This paper illustrates Woodin’s solutions to the problem, starting in Sect. 3 with his 1999–2004 argument that Cantor’s hypothesis about the continuum was incorrect. From 2010 onwards, Woodin presents a very different argument, an argument that Cantor’s hypothesis is in fact true. This argument is still incomplete, but according to Woodin, some of the philosophical issues surrounding the Continuum Problem have been reduced to precise mathematical questions, questions that are, unlike Cantor’s hypothesis, solvable from our current theory of sets.


Canonical Theory Force Extension Large Cardinal Measurable Cardinal Proper Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I would like to thank Brendan Larvor, Dominik Adolf, Jeremy Grey and José Ferreiós for their helpful comments.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.HatfieldUK

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