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STW naturally embodies the mechanisms of general<jats:italic>predicate application\/abstraction<\/jats:italic><jats:italic>on<\/jats:italic>a par with<jats:italic>function application\/abstraction<\/jats:italic>; in addition, it allows non-trivial constructions, inspired by generalized recursion theory. As a consequence, STW provides a smooth inner model for Myhill's systems with levels of implication.<\/jats:p>","DOI":"10.2307\/2275216","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:48:26Z","timestamp":1146955706000},"page":"477-513","source":"Crossref","is-referenced-by-count":5,"title":["Extending the first-order theory of combinators with self-referential truth"],"prefix":"10.1017","volume":"58","author":[{"given":"Andrea","family":"Cantini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200021290_ref022","doi-asserted-by":"publisher","DOI":"10.2307\/2024634"},{"key":"S0022481200021290_ref032","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-1171-0_10"},{"key":"S0022481200021290_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90040-6"},{"key":"S0022481200021290_ref011","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19890350202"},{"key":"S0022481200021290_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68952-9"},{"key":"S0022481200021290_ref012","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19920380109"},{"key":"S0022481200021290_ref029","first-page":"3","volume-title":"To H. 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