{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T17:25:26Z","timestamp":1694625926560},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":9873,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1987,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper introduces, as an alternative to the (absolutely) lawless sequences of Kreisel and Troelstra, a notion of choice sequence lawless with respect to a given class <jats:inline-graphic xmlns:xlink=\"https:\/\/2.zoppoz.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030000_inline1.png\" \/> of lawlike sequences. For countable <jats:inline-graphic xmlns:xlink=\"https:\/\/2.zoppoz.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030000_inline1.png\" \/>, the class of <jats:inline-graphic xmlns:xlink=\"https:\/\/2.zoppoz.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030000_inline1.png\" \/>-lawless sequences is comeager in the sense of Baire. If a particular well-ordered class <jats:inline-graphic xmlns:xlink=\"https:\/\/2.zoppoz.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030000_inline2.png\" \/> of sequences, generated by iterating definability over the continuum, is countable then the <jats:inline-graphic xmlns:xlink=\"https:\/\/2.zoppoz.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200030000_inline2.png\" \/>-lawless sequences satisfy the axiom of open data and the continuity principle for functions from lawless to lawlike sequences, but fail to satisfy Troelstra's extension principle. Classical reasoning is used.<\/jats:p>","DOI":"10.2307\/2273863","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:20:33Z","timestamp":1146954033000},"page":"68-88","source":"Crossref","is-referenced-by-count":3,"title":["Relative lawlessness in intuitionistic analysis"],"prefix":"10.1017","volume":"52","author":[{"given":"Joan Rand","family":"Moschovakis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200030000_bib013","doi-asserted-by":"publisher","DOI":"10.1007\/BF00247189"},{"key":"S0022481200030000_bib012","volume-title":"Choice sequences: a chapter of intuitionistic mathematics","author":"Troelstra","year":"1977"},{"key":"S0022481200030000_bib001","unstructured":"Brouwer, L. E. J. 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