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Everybody who catches a fleeting glimpse of Woodin's central papers on Ultimate $L$ (i.e. Suitable Extender Models I & II), admits that they aren't so tempting for lazy readers who don't like to deal with a lot of technicalities in their very first approach towards such an important topic.

On the other hand there are a lot of lazy but curious readers (like me) out there who seek royal roads leading to the main ideas of such long technical papers; the descriptive articles explaining the history, philosophy and general ideas behind the proofs and related conjectures (e.g. $HOD$ conjecture).

In this direction a simple Googling brings up several related articles and blog posts as well as uncountablly many lecture slide shows (mainly by Woodin himself) including the followings:

This question is intended to provide a list of descriptive articles on Woodin's Ultimate $L$ project. Please let me know if you are aware of any related under preparation article too.

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The latest issue of the Bulletin of Symbolic Logic has a long article by Woodin on Ultimate L:

WOODIN, W. (2017). IN SEARCH OF ULTIMATE-L THE 19TH MIDRASHA MATHEMATICAE LECTURES. The Bulletin of Symbolic Logic, 23(1), 1-109. doi:10.1017/bsl.2016.34

Might not be a royal road, though!

EDIT (David Roberts): As given in Mohammad Golshani's answer, free version here (pdf link, Wayback Machine).

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  • $\begingroup$ (+1) Seems really interesting! Thanks, Todd! $\endgroup$ – Morteza Azad May 15 '17 at 5:42
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You may also look at the following:

1) How Woodin changed his mind: new thoughts on the continuum hypothesis.

2) Tutorial outline: suitable extender sequences. Computational prospects of infinity. Part I. Tutorials, 195–253.

3) The weak ultimate L conjecture. Infinity, computability, and metamathematics, 309–329, Tributes, 23, Coll. Publ., London, 2014.

Regarding reference 3, the following is the review of it in Mathscinet by Kanamori:

The author provides an accessible, very helpful account of pivotal issues surrounding his current work toward the inner model "Ultimate L''. Most of the work appeared in his first long paper on suitable extender sequences [J. Math. Log. 10 (2010), no. 1-2, 101–339; MR2802084] in a general, very technical context, and here, in 20 pages, the author provides a thematically clear line through the heart of the main issues.


Regarding works in preparation, I may refer to the references given in Woodin's paper mentioned by Todd Eisworth (see also http://nrs.harvard.edu/urn-3:HUL.InstRepos:34649600 for an open access to the paper). You can see:

W. Hugh Woodin. The Axiom V = Ultimate-L. In preparation, 2016.

W. Hugh Woodin. Fine Structure at the Finite Levels of Supercompactness. 710 pages, 2016.

W. Hugh Woodin. The Ultimate-L Conjecture. 419 pages, 2016.

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    $\begingroup$ (+1) Thank you, Mohammad! It is worth mentioning that there is a review of Woodin's "The realm of the infinite" by Caicedo too. $\endgroup$ – Morteza Azad May 15 '17 at 6:03

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