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Great Question! Finally someone asks the simplest questions, which almost invariably are the real critical ones (if I cannot explain a great idea to an intelligent man in minutes, it simply means I do not understand it).

Tim, you have no idea how many thoughts your fantastic post has generated in my mind in the last 20 hours. Shelah 's dream can be made reality, but it ain't easy, though now at least I have some clue as to how to begin.

Great Question! Finally someone asks the simplest questions, which almost invariably are the real critical ones (if I cannot explain a great idea to an intelligent person in minutes, it simply means I do not understand it).

Tim, you have no idea how many thoughts your fantastic post has generated in my mind in the last 20 hours. Shelah's dream can be made reality, but it ain't easy, though now at least I have some clue as to how to begin.

ADDENDUM: SHELAH's LOGICAL DREAM (see commentary of Tim Chow)

Tim, you have no idea how many thoughts your fantastic post has generated in my mind in the last 20 hours. Shelah 's dream can be made reality, but it ain't easy, though now at least I have some clue as to how to begin.

It is the "virus control method": suppose you take M and throw in some G which is living in the truncated V cone where M lives. Add G. The very moment you add it, you are forced to add all sets which are G-constructibles in alpha steps, where alpha is any ordinal in M. Now, let us say that the most lethal viral attack perpetrated by G is that one of these new sets is exactly alpha_0, the first ordinal not in M, in other words G or its definable sets code a well order of type alpha_0.

If one carries out the analysis I have just sketched, the conjecture would be that a G which does not cause any damage is a set which is as close as possible to be definable in M already, in some sense to be made precise,but that goes along Cohen's intuition, namely that although G is not M-constructible, all its fragments are.

If this plan can be implemented, it would show that forcing is indeed unique, unless.... unless some other crazy idea come into play

Let me start with a historical background: in the 90s I talked with Stan Tennenbaum about Forcing, hoping to (finally!) understand it (did not go too far) . Here is what he told me (not verbatim): during those times,late 50s and very early 50s, several folks were trying their hand to prove independence.

LAST NOTE One of my favorite books in Science Fiction was written by the set theorist converted to writer, Dr. Rudy Rucker. The book is called White Light, and is a big celebration of Cantorian Set Theory written by an insider. It just misses one pearl, the most glorious one: Forcing. Who know, someone here, perhaps you, will write the sequel to Whute Light and show the splendor of Cohen's idea not only to "ordinary mathematicians" but to everybody...

Let me start with a historical background: in the 90s I talked with Stan Tennenbaum about Forcing, hoping to (finally!) understand it (did not go too far) . Here is what he told me (not verbatim): during those times,late 50s and very early 60s, several folks were trying their hand to prove independence.

LAST NOTE One of my favorite books in Science Fiction was written by the set theorist converted to writer, Dr. Rudy Rucker. The book is called White Light, and is a big celebration of Cantorian Set Theory written by an insider. It just misses one pearl, the most glorious one: Forcing. Who knows, someone here, perhaps you, will write the sequel to White Light and show the splendor of Cohen's idea not only to "ordinary mathematicians" but to everybody...