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Work within the type-theoretic tradition, in the style of<jats:italic>Principia Mathematica<\/jats:italic>, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics of axiomatic theories in the 1930s, by two proponents of the type-theoretic tradition (Carnap and Tarski) and two proponents of the first-order tradition (G\u00f6del and Hilbert), we argue that, instead, the move from type theory to first-order logic is better understood as a gradual transformation, and further, that the contributions to semantics made in the type-theoretic tradition should be seen as central to the evolution of model theory.<\/jats:p>","DOI":"10.1017\/s1079898600010568","type":"journal-article","created":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T08:31:20Z","timestamp":1469694680000},"page":"433-472","source":"Crossref","is-referenced-by-count":10,"title":["Logic in the 1930s: Type Theory and Model Theory"],"prefix":"10.1017","volume":"19","author":[{"given":"Georg","family":"Schiemer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erich H.","family":"Reck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,9,5]]},"reference":[{"key":"S1079898600010568_ref060","doi-asserted-by":"publisher","DOI":"10.1007\/s10670-012-9365-8"},{"key":"S1079898600010568_ref054","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-004-7801-1"},{"key":"S1079898600010568_ref052","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2866-9"},{"key":"S1079898600010568_ref020","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199296309.003.0004"},{"key":"S1079898600010568_ref019","doi-asserted-by":"publisher","DOI":"10.1080\/01445349408837233"},{"key":"S1079898600010568_ref017","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139172240"},{"key":"S1079898600010568_ref003","first-page":"23","volume-title":"Synthese","volume":"159","author":"Awodey","year":"2007"},{"key":"S1079898600010568_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9934-4"},{"key":"S1079898600010568_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BF02538231"},{"key":"S1079898600010568_ref027","volume-title":"Collected Works, Volume I: Publications 1929\u20131936","author":"G\u00f6del","year":"1986"},{"key":"S1079898600010568_ref069","first-page":"81","article-title":"Arithmetical extensions of relational systems","volume":"13","author":"Tarski","year":"1957","journal-title":"Compositio Mathematica"},{"key":"S1079898600010568_ref005","doi-asserted-by":"publisher","DOI":"10.1080\/01445340210146889"},{"key":"S1079898600010568_ref065","first-page":"1","article-title":"\u00dcber den Begriff der logischen Folgerung","volume":"7","author":"Tarski","year":"1936","journal-title":"Actes du Congr\u00e9s International de Philosophie Scientifique"},{"key":"S1079898600010568_ref006","doi-asserted-by":"crossref","DOI":"10.1515\/9781400826186","volume-title":"The birth of model theory. 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