most recent 30 from http://mathoverflow.net 2013-05-25T00:58:53Z http://mathoverflow.net/feeds/user/25551 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/104089/generalizing-the-ultrapower protologician 2012-08-06T09:07:10Z 2012-08-07T23:28:28Z

<p>Given an 2-valued measure $\mu$ on a set $I$, and structures $M_i \ (i \in I)$, one can construct the ultrapower $\prod_{i\in I}M_i / U$ (where $U$ is the ultrafilter associated with $\mu$.) One can then prove nice theorems about this structure - e,g, Łoś's theorem.</p> <p>But suppose now that rather than beginning with a 2-valued measure, we begin with a real valued measure on the set $I$, and structures $M_i \ (i \in I)$. Is there any sort of analagous structure that we can build and prove useful results about?</p>