{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:19:33Z","timestamp":1758824373217},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8593,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a finite lexicon <jats:italic>L<\/jats:italic> of relational symbols and equality, one may view the collection of all <jats:italic>L<\/jats:italic>-structures on the set of natural numbers <jats:italic>\u03c9<\/jats:italic> as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on <jats:italic>\u03c9<\/jats:italic>. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on <jats:italic>\u03c9<\/jats:italic> is ubiquitous in the set of linear orderings on <jats:italic>\u03c9<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2274467","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:36:50Z","timestamp":1146940610000},"page":"948-986","source":"Crossref","is-referenced-by-count":5,"title":["Notions of relative ubiquity for invariant sets of relational structures"],"prefix":"10.1017","volume":"55","author":[{"given":"Paul","family":"Bankston","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wim","family":"Ruitenburg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025494_ref027","first-page":"540\u2013542","article-title":"Sur certaines relations qui g\u00e9n\u00e9ralisent l'ordre des nombres rationnels","volume":"237","author":"Fra\u00efss\u00e9","year":"1953","journal-title":"Comptes Rendus Hebdomadaires des S\u00e9ances de l'Acad\u00e9mie des Sciences (Paris)"},{"key":"S0022481200025494_ref024","volume-title":"General topology","author":"Willard","year":"1970"},{"key":"S0022481200025494_ref018","first-page":"158\u2013163","article-title":"The Banach-Mazur game and Banach category theorem","volume":"3","author":"Oxtoby","year":"1957","journal-title":"Contributions to the theory of games"},{"key":"S0022481200025494_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(86)90046-8"},{"key":"S0022481200025494_ref014","doi-asserted-by":"publisher","DOI":"10.2307\/1971035"},{"key":"S0022481200025494_ref021","unstructured":"[21] Slattery M. (private communication)."},{"key":"S0022481200025494_ref011","first-page":"47\u2013103","volume-title":"Handbook of mathematical logic","author":"Keisler","year":"1977"},{"key":"S0022481200025494_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9440-2"},{"key":"S0022481200025494_ref002","volume-title":"Principles of combinatorics","author":"Berge","year":"1971"},{"key":"S0022481200025494_ref005","first-page":"85\u2013101","volume-title":"Advances in game theory","author":"Davis","year":"1964"},{"key":"S0022481200025494_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90008-2"},{"key":"S0022481200025494_ref028","doi-asserted-by":"publisher","DOI":"10.1007\/BF02582937"},{"key":"S0022481200025494_ref006","first-page":"50\u201358","volume":"41","author":"Fagin","year":"1976","journal-title":"Probabilities on finite models"},{"key":"S0022481200025494_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759729"},{"key":"S0022481200025494_ref009","volume-title":"Building models by games","author":"Hodges","year":"1985"},{"key":"S0022481200025494_ref026","first-page":"158\u2013169","volume-title":"The theory of models","author":"Keisler","year":"1965"},{"key":"S0022481200025494_ref004","volume-title":"Seminar talk","author":"Cameron","year":"1984"},{"key":"S0022481200025494_ref020","unstructured":"[20] Simms J. (private communication)."},{"key":"S0022481200025494_ref023","doi-asserted-by":"publisher","DOI":"10.4064\/fm-82-3-269-294"},{"key":"S0022481200025494_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(80)90014-5"},{"key":"S0022481200025494_ref013","first-page":"139\u2013180","volume-title":"Handbook of mathematical logic","author":"Macintyre","year":"1977"},{"key":"S0022481200025494_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-9964-7"},{"key":"S0022481200025494_ref010","first-page":"222\u2013230","volume":"53","author":"Hodkinson","year":"1988","journal-title":"Relational structures determined by their finite induced substructures"},{"key":"S0022481200025494_ref016","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870217"},{"key":"S0022481200025494_ref022","first-page":"227\u2013276","article-title":"Topological games: on the 50th anniversary of the Banach-Mazur game","volume":"17","author":"Telgarsky","year":"1987","journal-title":"Rocky Mountain Journal of Mathematics"},{"key":"S0022481200025494_ref003","first-page":"65\u201379","volume-title":"Graph theory and combinatorics (Proceedings of the Cambridge combinatorics conference in honor of Paul Erd\u00f6s","author":"Cameron","year":"1984"},{"key":"S0022481200025494_ref017","unstructured":"[17] Nelson E. 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