Geodesic
Letters of a~Bi-rationalist. VII~Ordered Termination
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 184-208

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To construct a resulting model in the LMMP, it is sufficient to prove the existence of log flips and their termination for some sequences. We prove that the LMMP in dimension $d-1$ and the termination of terminal log flips in dimension $d$ imply, for any log pair of dimension $d$, the existence of a resulting model: a strictly log minimal model or a strictly log terminal Mori log fibration, and imply the existence of log flips in dimension $d+1$. As a consequence, we prove the existence of a resulting model of 4-fold log pairs, the existence of log flips in dimension 5, and Geography of log models in dimension 4. 
@article{TM_2009_264_a18,
     author = {V. V. Shokurov},
     title = {Letters of {a~Bi-rationalist.} {VII~Ordered} {Termination}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {184--208},
     publisher = {mathdoc},
     volume = {264},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_264_a18/}
}
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V. V. Shokurov. Letters of a~Bi-rationalist. VII~Ordered Termination. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 184-208. http://geodesic.mathdoc.fr/item/TM_2009_264_a18/