{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T18:47:54Z","timestamp":1772304474713,"version":"3.50.1"},"reference-count":19,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2005,8,3]],"date-time":"2005-08-03T00:00:00Z","timestamp":1123027200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2005,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Specker sequences are constructive, increasing, bounded sequences of rationals that do not converge to any constructive real. A sequence is said to be <jats:italic>a strong Specker sequence<\/jats:italic> if it is Specker and eventually bounded away from every constructive real. Within Bishop's constructive mathematics we investigate non\u2010decreasing, bounded sequences of rationals that eventually avoid sets that are unions of (countable) sequences of intervals with rational endpoints. This yields surprisingly straightforward proofs of certain basic results fromconstructive mathematics. Within Russian constructivism, we show how to use this general method to generate Specker sequences. Furthermore, we show that any nonvoid subset of the constructive reals that has no isolated points contains a strictly increasing sequence that is eventually bounded away from every constructive real. If every neighborhood of every point in the subset contains a rational number different from that point, the subset contains a strong Specker sequence. (\u00a9 2005 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200410048","type":"journal-article","created":{"date-parts":[[2005,8,3]],"date-time":"2005-08-03T22:20:57Z","timestamp":1123107657000},"page":"532-540","source":"Crossref","is-referenced-by-count":2,"title":["Specker sequences revisited"],"prefix":"10.1002","volume":"51","author":[{"given":"Jakob G.","family":"Simonsen","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,8,3]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"O.Aberth Computable Analysis (McGraw\u2010Hill New York 1980)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"E.Bishop andD.Bridges Constructive Analysis. 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G.Hocking andG. S.Young Topology (Dover Publications Inc. New York 1988)."},{"key":"e_1_2_1_9_2","first-page":"1106","article-title":"Ensembles r\u00e9cursivements m\u00e9surables et ensembles r\u00e9cursivements ouverts ou ferm\u00e9s","volume":"245","author":"Kreisel G.","year":"1957","journal-title":"C. R. Acad. Sci. Paris, Ser. A \u2013 B"},{"key":"e_1_2_1_10_2","unstructured":"K.\u2010I.Ko Complexity Theory of Real Functions (Birkh\u00e4user Boston 1991)."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(66)80018-9"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-3577(98)80037-2"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.2307\/2267043"},{"key":"e_1_2_1_14_2","unstructured":"E.Specker Der Satz vom Maximum in der rekursiven Analysis. In: Constructivity in Mathematics (A. 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