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Abstract I am always very enthusiastic about my last work, but since Dec 87 I am enthusiastic mainly about the work presented here. Let me try to share this with you, the reader. If we interpret “true” by “is provable in ZFC” (the usual axioms of set theory), as I do, then a large part of set theory which is done today does not deal directly with true theorems-it deals, rather, with a huge machinery for building counterexamples (forcing possible universes) or with “thin” universes (inner models). Very often the answer to “can this happen?” is “it depends”. Now, I believe that this phenomenon is inevitable, and expresses a deep phase of the development of set theory, which resulted in many fascinating theorems (and also in quite a few proofs of mine). However, there is still some uneasiness about it. A way to express it is to say that if Cantor would have risen from his grave today, he would not just have problems understanding the proofs of modern theorems-he would not understand what the theorems actually say. We do not try to fight this prejudice here, as it works in our favour.