Related papers: Notes on the log minimal model program

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This paper has been withdrawn by the author. The most updated version can be accessed by arXiv:1806.07290.

This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.

The paper was withdrawn because of its significant overlap with a paper appeared recently.

This submission has been withdrawn by arXiv admin. It is a verbatim copy of arXiv:0912.1810 with only the author name and title changed.

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This submission has been withdrawn at the request of the author.

This paper has been withdrawn by the author due to rewritting and skipping crucial sign errors.

This submission has been withdrawn by arXiv administration.

Again, this preprint has been combined with hep-ph/0207106, which is co-authored by both of us. Therefore, this preprint has been withdrawn. Readers are welcome to refer to hep-ph/0207106.

This paper has been withdrawn as it has been superseded by postings arXiv:quant-ph/0702147 and arXiv:0712.2935

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This paper was withdrawn on 20.11.97.

This paper has been withdrawn by the author. There is an error on page 3 in the last inequality before Lemma 1.1.

This paper has been withdrawn by the author, as it is now incorporated in 0901.4506 (v4)

This paper has been withdrawn by the author due to an error in the proof of Theorem 6.

This paper has been withdrawn due to a critical error discovered in Theorem 4.21. Anyone with a historical or pragamatic interest in prior "negative results", however - e.g., failed proof attempts relating to the (in)consistency of ZF or…

This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2080.