{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:30:56Z","timestamp":1760887856173},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":5615,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[1998,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We develop a constructive version of nonstandard analysis, extending Bishop's constructive analysis with infinitesimal methods. A full transfer principle and a strong idealisation principle are obtained by using a sheaf-theoretic construction due to I. Moerdijk. The construction is, in a precise sense, a reduced power with variable filter structure. We avoid the nonconstructive standard part map by the use of nonstandard hulls. This leads to an infinitesimal analysis which includes nonconstructive theorems such as the Heine\u2013Borel theorem, the Cauchy\u2013Peano existence theorem for ordinary differential equations and the exact intermediate-value theorem, while it at the same time provides constructive results for concrete statements. A nonstandard measure theory which is considerably simpler than that of Bishop and Cheng is developed within this context.<\/jats:p>","DOI":"10.2307\/421031","type":"journal-article","created":{"date-parts":[[2006,5,7]],"date-time":"2006-05-07T07:11:46Z","timestamp":1146985906000},"page":"233-272","source":"Crossref","is-referenced-by-count":34,"title":["Developments in Constructive Nonstandard Analysis"],"prefix":"10.1017","volume":"4","author":[{"given":"Erik","family":"Palmgren","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600007216_ref023","first-page":"369","volume-title":"M\u00e9thodes et analyse non 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