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There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the <jats:italic>Mouse Set Conjecture<\/jats:italic> (MSC). One particular motivation for resolving MSC is that it provides grounds for solving the <jats:italic>inner model problem<\/jats:italic> which dates back to 1960s. There have been some new partial results on MSC and the methods used to prove the new instances suggest a general program for solving the full conjecture. It is then our goal to communicate the ideas of this program to the community at large.<\/jats:p>","DOI":"10.2178\/bsl.1901010","type":"journal-article","created":{"date-parts":[[2013,5,16]],"date-time":"2013-05-16T15:07:49Z","timestamp":1368716869000},"page":"1-55","source":"Crossref","is-referenced-by-count":15,"title":["Descriptive inner model theory"],"prefix":"10.1017","volume":"19","author":[{"given":"Grigor","family":"Sargsyan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,9,5]]},"reference":[{"key":"S1079898600009045_ref038","first-page":"485","volume":"7","author":"Schimmerling","year":"2001","journal-title":"The ABC's of mice"},{"key":"S1079898600009045_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9754-0_15"},{"key":"S1079898600009045_ref025","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21903-4"},{"key":"S1079898600009045_ref046","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1129642125"},{"key":"S1079898600009045_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/2275336"},{"key":"S1079898600009045_ref020","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0071697"},{"key":"S1079898600009045_ref031","doi-asserted-by":"publisher","DOI":"10.2307\/2586477"},{"key":"S1079898600009045_ref033","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12013-2"},{"key":"S1079898600009045_ref023","doi-asserted-by":"publisher","DOI":"10.2307\/2273452"},{"key":"S1079898600009045_ref032","unstructured":"Rudominer Mitchell , Mouse sets definable in L(\u211d), Ph.D. thesis. 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