{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T23:05:24Z","timestamp":1648940724705},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T00:00:00Z","timestamp":1236124800000},"content-version":"unspecified","delay-in-days":6212,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[1992,3]]},"abstract":"Based on a categorical semantics for impredicative calculi of dependent types we prove several dependence and independence results. Especially we prove that there exists a model where all usual syntactical concepts can be interpreted with only one exception: in the model the strong sum of a family of propositions indexed over a proposition need not be isomorphic to a proposition again.<\/jats:p>The method of proof consists of restricting the set of propositions in the well known PERw model due to E. Moggi. The subsets of PERw considered in this paper are inspired by the subset ExpO of PERw introduced by Freyd et al<\/jats:italic>.<\/jats:p>Finally we show that a weak and a strong notion of sub-locally-cartesian-closed-category coincide under rather mild completeness conditions.<\/jats:p>","DOI":"10.1017\/s0960129500001122","type":"journal-article","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T04:02:44Z","timestamp":1236139364000},"page":"29-54","source":"Crossref","is-referenced-by-count":2,"title":["Dependence and independence results for (impredicative) calculi of dependent types"],"prefix":"10.1017","volume":"2","author":[{"given":"Thomas","family":"Streicher","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,4]]},"reference":[{"key":"S0960129500001122_ref009","unstructured":"Rosolini G. (1988) About modest sets. Preprint."},{"key":"S0960129500001122_ref010","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100061284"},{"key":"S0960129500001122_ref005","doi-asserted-by":"crossref","unstructured":"Hyland M. and Pitts A. (1989) The theory of constructions: categorical semantics and topostheoretic models. In: Proc. Conf. Categories in Computer Science and Logic. Contemp. Math. Amer. Math. Soc.","DOI":"10.1090\/conm\/092\/1003199"},{"key":"S0960129500001122_ref012","unstructured":"Streicher T. (1988) Correctness and completeness of a categorical semantics of the calculus of constructions. PhD Thesis, University of Passau."},{"key":"S0960129500001122_ref003","unstructured":"Ehrhard T. (1989) Dictoses. In: Proc. 3rd Workshop on Category Theory in Computer Science. Springer Lecture Notes in Computer Science."},{"key":"S0960129500001122_ref002","volume-title":"Proc. 3rd LICS Conf","author":"Ehrhard","year":"1988"},{"key":"S0960129500001122_ref001","volume-title":"Proc. 1st LICS Conf","author":"Coquand","year":"1986"},{"key":"S0960129500001122_ref007","volume-title":"Studies in Proof Theory","author":"Martin-L\u00f6f","year":"1984"},{"key":"S0960129500001122_ref011","doi-asserted-by":"crossref","unstructured":"Seely R. (1987) Categorical semantics for higher order polymorphic lambda calculus. J. Symbolic Logic.","DOI":"10.2307\/2273831"},{"key":"S0960129500001122_ref006","article-title":"Universe models and initial model semantics for the second order polymorphic lambda calculus","volume":"58","author":"Meseguer","year":"1988","journal-title":"Abstracts of papers presented to A.M.S"},{"key":"S0960129500001122_ref004","volume-title":"Domains in PER","author":"Freyd","year":"1989"},{"key":"S0960129500001122_ref013","unstructured":"Seely R. (1989) Independence results for calculi of dependent types. In: Proc. 3rd Workshop on Category Theory in Computer Science. Springer Lecture Notes in Computer Science."},{"key":"S0960129500001122_ref008","article-title":"Polymorphism is set-theoretic, constructively","volume":"283","author":"Pitts","year":"1987","journal-title":"Proc. Conf. Category Theory and Computer Science, Edinburgh 1987. Springer Lecture Notes in Computer Science"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129500001122","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T18:19:01Z","timestamp":1558030741000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129500001122\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,3]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,3]]}},"alternative-id":["S0960129500001122"],"URL":"https:\/\/doi.org\/10.1017\/s0960129500001122","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,3]]}}}