{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T17:38:27Z","timestamp":1751391507541},"reference-count":0,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T00:00:00Z","timestamp":1512000000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a topological Ramsey space , we extend the notion of semiselective coideal to sets  and study conditions for  that will enable us to make the structure  a Ramsey space (not necessarily topological) and also study forcing notions related to  which will satisfy abstract versions of interesting properties of the corresponding forcing notions in the realm of Ellentuck's space (cf. [][]). This extends results from [][] to the most general context of topological Ramsey spaces. As applications, we prove that for every topological Ramsey space , under suitable large cardinal hypotheses every semiselective ultrafilter  is generic over ; and that given a semiselective coideal , every definable subset of  is \u2010Ramsey. This generalizes the corresponding results for the case when  is equal to Ellentuck's space (cf. [][]).<\/jats:p>","DOI":"10.1002\/malq.201500086","type":"journal-article","created":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T13:02:45Z","timestamp":1512046965000},"page":"384-396","source":"Crossref","is-referenced-by-count":6,"title":["Local Ramsey theory: an abstract approach"],"prefix":"10.1002","volume":"63","author":[{"given":"Carlos","family":"Di Prisco","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas Instituto Venezolano de Investigaciones Cient\u00edficas Altos de Pipe Miranda Venezuela"},{"name":"Departamento de Matem\u00e1ticas Universidad de Los Andes 111711 Bogot\u00e1 Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 G.","family":"Mijares","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Statistical Sciences University of Colorado Denver 1201 Larimer Street Denver CO 80204 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jes\u00fas","family":"Nieto","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas Universidad Sim\u00f3n Bol\u00edvar Sartenejas Baruta Miranda Venezuela"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2017,11,30]]},"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201500086","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201500086","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T16:50:41Z","timestamp":1696006241000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201500086"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,30]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["10.1002\/malq.201500086"],"URL":"https:\/\/doi.org\/10.1002\/malq.201500086","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,30]]}}}