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I'm cross-posting this from Mathoverflow. Since I'm asking for recent developments, it seems best to have answers in both sites.

The website Formalizing 100 Theorems by Freek Wiedijk contains a list of some theorems that were chosen at some point as good candidates for formalization (because of their complexity, their importance, etc.) This website seems to be updated very often.

Among the proofs not yet formalized is that of the independence of the Continuum Hypothesis from the axioms of set theory.

What is the current state of the formalization of the independence of $\mathit{CH}$ from $\mathit{ZFC}$?

I browsed Mathoverflow for more information, and I found this recent question, as well as this one and this, and an answer in this site. But I couldn't find information directly concerned with my question.

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    $\begingroup$ How about the question of mine? There are no answer but Andrej comments on it. $\endgroup$
    – Hanul Jeon
    Commented Mar 27, 2017 at 12:14
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    $\begingroup$ MathOverflow: mathoverflow.net/questions/265435/… $\endgroup$
    – Asaf Karagila ♦
    Commented Mar 27, 2017 at 13:25
  • $\begingroup$ @AsafKaragila Thanks, I forgot to add the link. $\endgroup$
    – Pedro Sánchez Terraf
    Commented Mar 27, 2017 at 16:08
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    $\begingroup$ @PedroSánchezTerraf: Freek's list is not intended to highlight the most difficult problems. You are, however, right that it is a nice source of information and that Freek keeps it up to date. And you are right that some MSE users are involved in "this kind of business": in fact, I can think of at least 2. Can you? $\ddot{\smile}$ $\endgroup$
    – Rob Arthan
    Commented Mar 28, 2017 at 20:00
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    $\begingroup$ I think your edit should be an answer. $\endgroup$
    – Z. A. K.
    Commented Mar 19 at 23:36

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As per Zoltan Kocsis' suggestion, I'm answering the question with an updated on our developments (formerly, this was an edit to the OP).

We finished our formalization of the countable transitive model approach to forcing and the independence of $\mathit{CH}$. The paper is available here and at the arXiv.

The answer to the MO question linked above contains the info about the first formalization of the independence, by Han and van Doorn.

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