{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:35:21Z","timestamp":1747150521354,"version":"3.40.5"},"reference-count":6,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2022,2,11]],"date-time":"2022-02-11T00:00:00Z","timestamp":1644537600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2022,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study notions of genericity in models of , inspired by lines of inquiry initiated by Chatzidakis and Pillay and continued by Dolich, Miller and Steinhorn in general model\u2010theoretic contexts. These papers studied the theories obtained by adding a \u201crandom\u201d predicate to a class of structures. Chatzidakis and Pillay axiomatized the theories obtained in this way. In this article, we look at the subsets of models of  which satisfy the axiomatization given by Chatzidakis and Pillay; we refer to these subsets in models of  as CP\u2010generics. We study a more natural property, called strong CP\u2010genericity, which implies CP\u2010genericity. We use an arithmetic version of Cohen forcing to construct (strong) CP\u2010generics with various properties, including ones in which every element of the model is definable in the expansion, and, on the other extreme, ones in which the definable closure relation is\u00a0unchanged.<\/jats:p>","DOI":"10.1002\/malq.202100051","type":"journal-article","created":{"date-parts":[[2022,2,12]],"date-time":"2022-02-12T03:45:20Z","timestamp":1644637520000},"page":"171-177","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["CP\u2010generic expansions of models of Peano Arithmetic"],"prefix":"10.1002","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8993-0025","authenticated-orcid":false,"given":"Athar","family":"Abdul\u2010Quader","sequence":"first","affiliation":[{"name":"School of Natural and Social Sciences SUNY Purchase College 735 Anderson Hill Road Purchase NY 10577 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James H.","family":"Schmerl","sequence":"additional","affiliation":[{"name":"Department of Mathematics University of Connecticut Storrs CT 06269 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,2,11]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201800043"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(98)00021-9"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl.7802020"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2016.04.003"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.2307\/2275523"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198568278.001.0001"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.202100051","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.202100051","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.202100051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T21:46:41Z","timestamp":1693000001000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.202100051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,11]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,5]]}},"alternative-id":["10.1002\/malq.202100051"],"URL":"https:\/\/doi.org\/10.1002\/malq.202100051","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[2022,2,11]]},"assertion":[{"value":"2021-08-31","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-01-25","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-02-11","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}