{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:15:34Z","timestamp":1753884934129,"version":"3.41.2"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100003977","name":"the Israel Science Foundation","doi-asserted-by":"crossref","award":["1533\/14","1254\/18"],"award-info":[{"award-number":["1533\/14","1254\/18"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003977","name":"the Israel Science Foundation","doi-asserted-by":"crossref","award":["1838\/19"],"award-info":[{"award-number":["1838\/19"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the European Research Council","award":["338821"],"award-info":[{"award-number":["338821"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class (PC)-exact saturation meaningfully reflects combinatorial dividing lines. We study PC-exact saturation for stable and simple theories. Among other results, we show that PC-exact saturation characterizes the stability cardinals of size at least continuum of a countable stable theory and, additionally, that simple unstable theories have PC-exact saturation at singular cardinals satisfying mild set-theoretic hypotheses. This had previously been open even for the random graph. We characterize supersimplicity of countable theories in terms of having PC-exact saturation at singular cardinals of countable cofinality. We also consider the local analog of PC-exact saturation, showing that local PC-exact saturation for singular cardinals of countable cofinality characterizes supershort theories. <\/jats:p>","DOI":"10.1142\/s0219061322500209","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T09:18:28Z","timestamp":1655457508000},"source":"Crossref","is-referenced-by-count":0,"title":["Exact saturation in pseudo-elementary classes for simple and stable theories"],"prefix":"10.1142","volume":"23","author":[{"given":"Itay","family":"Kaplan","sequence":"first","affiliation":[{"name":"Einstein Institute of Mathematics, Hebrew University of Jerusalem, 91904, Jerusalem Israel"}]},{"given":"Nicholas","family":"Ramsey","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Notre Dame, South Bend, IN, 46617, USA"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[{"name":"Einstein Institute of Mathematics, Hebrew University of Jerusalem, 91904, Jerusalem Israel"}]}],"member":"219","published-online":{"date-parts":[[2022,9,27]]},"reference":[{"issue":"2","key":"S0219061322500209BIB001","doi-asserted-by":"crossref","first-page":"817","DOI":"10.2307\/2586503","volume":"64","author":"Buechler S.","year":"1999","journal-title":"J. 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