{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T15:06:30Z","timestamp":1649084790077},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2002,1,9]],"date-time":"2002-01-09T00:00:00Z","timestamp":1010534400000},"content-version":"unspecified","delay-in-days":39,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2001,12]]},"abstract":"<jats:p>This paper concerns the elimination of higher type quantifiers and gives two theorems. The \nfirst theorem shows that quantifiers in formulae of a specific form can be eliminated. The \nsecond theorem shows that quantifiers in formulae of a similar form cannot be eliminated, \nthat is, such formulae do not have an equivalent first-order formula. The proof is based on \nthe Ehrenfeucht game. These theorems are important for design of an interpreter of a \u03bd act, \nwhich is a representation of mathematical action. Moreover, even if the universe is assumed \nto be finite, these theorems hold.<\/jats:p>","DOI":"10.1017\/s0960129501003401","type":"journal-article","created":{"date-parts":[[2008,7,31]],"date-time":"2008-07-31T08:22:25Z","timestamp":1217492545000},"page":"771-779","source":"Crossref","is-referenced-by-count":0,"title":["On the elimination of some higher type quantifiers"],"prefix":"10.1017","volume":"11","author":[{"given":"YASUWO","family":"IKEDA","sequence":"first","affiliation":[]},{"given":"KOHJI","family":"TOMITA","sequence":"additional","affiliation":[]},{"given":"CHIHARU","family":"HOSONO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2002,1,9]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129501003401","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T21:36:02Z","timestamp":1557264962000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129501003401\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,12]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2001,12]]}},"alternative-id":["S0960129501003401"],"URL":"https:\/\/doi.org\/10.1017\/s0960129501003401","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,12]]}}}