{"id":19,"date":"2025-01-16T15:58:34","date_gmt":"2025-01-16T20:58:34","guid":{"rendered":"https:\/\/sites.nd.edu\/gabriel-day\/?page_id=19"},"modified":"2026-07-21T11:40:54","modified_gmt":"2026-07-21T15:40:54","slug":"research","status":"publish","type":"page","link":"https:\/\/sites.nd.edu\/gabriel-day\/research\/","title":{"rendered":"Research"},"content":{"rendered":"
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My work in philosophy of mathematics primarily investigates questions arising from the study of logic. Some recent and ongoing projects investigate what the field of model theory reveals about mathematical complexity, and how model theoretic “applications” unify mathematical phenomena such as well-behaved notions of dimension and independence.<\/p>\n\n\n\n

My mathematical research likewise concentrates on model theory, in particular, on generalizations of indiscernible sequences and tree properties. I have also investigated characterizations of “patterning properties” in model theory, such as straight definability<\/em>.<\/p>\n\n\n\n

In addition to these central research topics, my academic interests include the question of why people do mathematics (and how AI might change that), the 19th and 20th Century history and philosophy of logic and mathematics, and the writings and reception of Karl Marx.<\/p>\n\n\n\n

I completed Notre Dame\u2019s Joint PhD in Philosophy and Mathematics<\/a>, advised by Curtis Franks<\/a> and Nick Ramsey<\/a>. My dissertation includes both philosophical and mathematical contributions, on the central research topics mentioned above.<\/p>\n\n\n\n

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My work in philosophy of mathematics primarily investigates questions arising from the study of logic. Some recent and ongoing projects investigate what the field of model theory reveals about mathematical complexity, and how model theoretic “applications” unify mathematical phenomena such as well-behaved notions of dimension and independence. My mathematical research likewise concentrates on model theory, … Continue reading Research<\/span><\/a><\/p>\n","protected":false},"author":4973,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-19","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/gabriel-day\/wp-json\/wp\/v2\/pages\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/gabriel-day\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.nd.edu\/gabriel-day\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/gabriel-day\/wp-json\/wp\/v2\/users\/4973"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/gabriel-day\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":6,"href":"https:\/\/sites.nd.edu\/gabriel-day\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":68,"href":"https:\/\/sites.nd.edu\/gabriel-day\/wp-json\/wp\/v2\/pages\/19\/revisions\/68"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/gabriel-day\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}