Classification of properties of structures - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T03:28:50Z http://mathoverflow.net/feeds/question/11146 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/11146/classification-of-properties-of-structures Classification of properties of structures Hans Stricker 2010-01-08T14:30:32Z 2010-01-08T14:42:56Z <p>Is there a sensible classification of the properties of structures with a given signature $\sigma$, e.g. graphs with $\sigma = \lbrace R \rbrace$?</p> <p>For example like this:</p> <ol> <li><p>properties defined by first-order sentences over $\sigma$ (with or without specific syntactical properties)</p></li> <li><p>properties defined by monadic second-order sentences over $\sigma$ (with or without specific syntactical properties)</p></li> <li><p>properties stating the existence of another structure (of the same kind or another) and a specific <strike>mapping</strike> relation to it</p></li> <li><p>properties stating that a given structure invariant has a specific value </p></li> <li><p>properties stating that a given structure invariant has a specific property</p></li> </ol> <p>How can this list be expanded, can it be completed or can it never be exhaustive?</p>