tag:blogger.com,1999:blog-11295132.post114849148496422161..comments2024-02-24T01:46:31.188-08:00Comments on A Neighborhood of Infinity: Exceptional Objectssigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-11295132.post-1156622092830876302006-08-26T12:54:00.000-07:002006-08-26T12:54:00.000-07:00You said in your post:"What frequently happens is ...You said in your post:<BR/><BR/>"What frequently happens is that objects of a certain type are classified into a bunch of series with a handful of exceptional objects left over."<BR/><BR/>What frequently happens is something even more interesting: by extending the language and therefore increasing the number of "objects", it is possible to place old sporadic objects into new infinite families. In the new extended set-up we have a "bunch" of infinite series and a <I>finite number of new sporadic objectts</I>. This extension process continues ad infinitum. See a model-theoretic explanation of this phenomenon in a paper by Gregory Cherlin "Sporadic homogeneous structures". <BR/><BR/>http://www.rci.rutgers.edu/~cherlin/Publication/sporadic.pdf<BR/><BR/>His proof is crucially based on the classification of finite simple groups.Alexandre Borovikhttps://www.blogger.com/profile/11437354321695384127noreply@blogger.com