most recent 30 from http://mathoverflow.net 2013-06-18T06:47:24Z http://mathoverflow.net/feeds/question/102872 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/102872/local-character-of-tarski-vaught-for-tuples-in-excellent-classes o a 2012-07-22T14:43:58Z 2012-07-22T14:43:58Z

<p>In the book <a href="http://www.math.uic.edu/~jbaldwin/pub/AEClec.pdf" rel="nofollow">Baldwin, Categoricity in Abstract Elementary Classes</a> defines (Def.20.1,p.151) a notion of Tarski-Vaught extensions for tuples that generalises both independence and usual Tarski-Vaught extensions (Ex 20.4,p.152). </p> <p>Is there any "finite character" for Tarski-Vaught for tuples generalising finite character for independence(splitting) ? That is, a generalisation of Exercise 19.15,p.147 ? </p> <p>I would also be interested to see a proof of equivalence of definitions of a <i>good system</i> as defined by Baldwin and by Shelah in the original paper. </p>