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We give precise definitions and equivalences, saying what it means for properties such as PAC to be first order, study some examples (such as differentially closed fields) in detail, relate the material to generic automorphisms, and generalize a \u201cdescent theorem\u201d for pseudo-algebraically closed fields to the stable context. We also point out that the elementary invariants of pseudo-algebraically closed fields from [6] are also valid for pseudo-differentially closed fields.<\/jats:p>","DOI":"10.2178\/jsl\/1146620152","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:22:51Z","timestamp":1198081371000},"page":"460-472","source":"Crossref","is-referenced-by-count":10,"title":["On PAC and bounded substructures of a stable structure"],"prefix":"10.1017","volume":"71","author":[{"given":"Anand","family":"Pillay","sequence":"first","affiliation":[]},{"given":"Dominika","family":"Polkowska","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200006149_ref019","volume-title":"Model theory and applications","volume":"11","author":"Pillay","year":"2003"},{"key":"S0022481200006149_ref006","unstructured":"Cherlin G. , van den Dries L. , and Macintyre A. . 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