most recent 30 from http://mathoverflow.net 2013-05-24T14:12:39Z http://mathoverflow.net/feeds/user/24212 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/98775/ultimate-maximality-principle Lianna 2012-06-04T14:52:33Z 2012-06-04T15:31:49Z

<p>I wonder if it's possible to formulate an "ultimate" maximality principle (UMP) and prove its consistency. I envision UMP to express the idea that no matter how we enlarge the universe of set theory V (by any means e.g. set forcing, class forcing, infinite model theory), we would gain n o t h i n g. Let W be the ultimate enlargement of V. Then UMP would say that a statement is true in W iff it's true in V. So any statement that is true in W is already true in V.</p> <p>Questions: 1) Are there available reference in literature concerning UMP? 2) If not, what is the prospect of UMP in foundational research?</p>

http://mathoverflow.net/questions/98775/ultimate-maximality-principle/98776#98776 Lianna 2012-06-05T15:19:07Z 2012-06-05T15:19:07Z

Thank you for your extensive reply Joel.I just read the papers you mentioned above. It's very interesting. In your last paragraph, you mention that there is current work on maximality-type principles for class forcing and for arbitrary extensions. Are you talking about Sy. Friedman's work? He has a new paper on the Hyperuniverse program on his website.