{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:08:51Z","timestamp":1778717331410,"version":"3.51.4"},"reference-count":10,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2021,8,29]],"date-time":"2021-08-29T00:00:00Z","timestamp":1630195200000},"content-version":"vor","delay-in-days":28,"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":[[2021,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper answers several open questions around structures with o\u2010minimal open core. We construct an expansion of an o\u2010minimal structure  by a unary predicate such that its open core is a proper o\u2010minimal expansion of . We give an example of a structure that has an o\u2010minimal open core and the exchange property, yet defines a function whose graph is dense. Finally, we produce an example of a structure that has an o\u2010minimal open core and definable Skolem functions, but is not\u00a0o\u2010minimal.<\/jats:p>","DOI":"10.1002\/malq.202100008","type":"journal-article","created":{"date-parts":[[2021,8,29]],"date-time":"2021-08-29T22:21:02Z","timestamp":1630275662000},"page":"382-393","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Pathological examples of structures with o\u2010minimal open core"],"prefix":"10.1002","volume":"67","author":[{"given":"Alexi","family":"Block Gorman","sequence":"first","affiliation":[{"name":"University of Illinois at Urbana\u2010Champaign Department of Mathematics 1409 W. Green Street Urbana IL 61801"}]},{"given":"Erin","family":"Caulfield","sequence":"additional","affiliation":[{"name":"McMaster University Department of Mathematics &amp; Statistics 1280 Main Street West Hamilton Ontario Canada L8S 4K1"}]},{"given":"Philipp","family":"Hieronymi","sequence":"additional","affiliation":[{"name":"University of Illinois at Urbana\u2010Champaign Department of Mathematics 1409 W. 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