Answer by Ralf Schindler for Solutions to the Continuum Hypothesis
In Aug. 2020, I gave a talk at Wuhan with the title "How many real numbers are there?", taking into account my result with D. Asperó on MM++ => (*). There is a recording:...
View ArticleAnswer by Grigor for Solutions to the Continuum Hypothesis
my answer was too fast, and so i deleted it, but it seems that Gil refers to it, so i will again very quickly explain the matter.in general, i agree with the view that some mathematicians express,...
View ArticleAnswer by Gro-Tsen for Solutions to the Continuum Hypothesis
Since this old question has been bumped to the front page, I'm surprised nobody so far mentioned the following opinion expressed by Paul Cohen at the end of his 1966 book Set Theory and the Continuum...
View ArticleAnswer by Mohammad Golshani for Solutions to the Continuum Hypothesis
Let me add in short details, views of three famous set theorists about the problem: Shelah’s answer: The question was wrong. The right question should be about othercombinatorial objects. There we can...
View ArticleAnswer by none for Solutions to the Continuum Hypothesis
This is a nice survey:http://logic.harvard.edu/EFI_CH.pdfKoellner, Peter (2011). "The Continuum Hypothesis". Exploring the Frontiers of Independence (Harvard lecture series).(Pasted from Wikipedia...
View ArticleAnswer by Justin Moore for Solutions to the Continuum Hypothesis
First I'll say a few words about forcing axioms and then I'll answer your question. Forcing axioms were developed to provide a unified framework to establish the consistency of a number of...
View ArticleAnswer by Gil Kalai for Solutions to the Continuum Hypothesis
Shelah's approach from his paper in his "The Generalized Continuum Hypothesis revisited", concerns mainly the generalized continuum hypothesis. His main theorem addresses an appealing variation of the...
View ArticleAnswer by mmm for Solutions to the Continuum Hypothesis
There is a recent (and unfinished) attempt to view the Shelah's approach to Continuum Hypothesis in terms of homotopy theory.
View ArticleAnswer by Joel David Hamkins for Solutions to the Continuum Hypothesis
Since you have already linked to some of the contemporaryprimary sources, where of course the full accounts of thoseviews can be found, let me interpret your question as arequest for summary accounts...
View ArticleAnswer by Andrés E. Caicedo for Solutions to the Continuum Hypothesis
(1) Patrick Dehornoy gave a nice talk at the Séminaire Bourbaki explaining Hugh Woodin's approach. It omits many technical details, so you may want to look at it before looking again at the Notices...
View ArticleAnswer by Simon Thomas for Solutions to the Continuum Hypothesis
The question of whether or not $2^{\aleph_{0}} = \aleph_{1}$ is not even considered in Shelah's approach. In fact, this question is regarded as part of the "white noise" which has distracted the...
View ArticleAnswer by Haim for Solutions to the Continuum Hypothesis
Regarding Shelah's approach, I believe that the following paper should be quite accessible to non-professionals: YOU CAN ENTER CANTOR’S PARADISE!Now, I have no idea how to explain Woodin's approach to...
View ArticleSolutions to the Continuum Hypothesis
Related MO questions: What is the general opinion on the Generalized Continuum Hypothesis? ; Completion of ZFC ; Complete resolutions of GCHHow far wrong could the Continuum Hypothesis be?When was the...
View ArticleAnswer by Grigor for Solutions to the Continuum Hypothesis
One probably should add that the continuum hypothesis depends a lot on how you ask it.$2^{\omega}=\omega_1$Every set of reals is either countable or has the same size as the continuum.To me, 1 is a...
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