{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T20:15:33Z","timestamp":1772828133919,"version":"3.50.1"},"reference-count":7,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2009,11,17]],"date-time":"2009-11-17T00:00:00Z","timestamp":1258416000000},"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":[[2009,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema (which we call <jats:bold>ED<\/jats:bold>) about intuitionistic decidability that asserts \u201cthere exists an intuitionistic enumerable set that is not intuitionistic decidable\u201d and show that the existence of a Specker sequence is equivalent to <jats:bold>ED<\/jats:bold>. We show that <jats:bold>ED<\/jats:bold> is consistent with some certain well known axioms of intuitionistic analysis as Weak Continuity Principle, bar induction, and Kripke Schema. Thus, the assumption of the existence of a Specker sequence is conceivable in intuitionistic analysis. We will also introduce the notion of double Specker sequence and study the existence of them (\u00a9 2009 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710094","type":"journal-article","created":{"date-parts":[[2009,11,18]],"date-time":"2009-11-18T00:15:31Z","timestamp":1258503331000},"page":"637-648","source":"Crossref","is-referenced-by-count":7,"title":["Decidability and Specker sequences in intuitionistic mathematics"],"prefix":"10.1002","volume":"55","author":[{"given":"Mohammad","family":"Ardeshir","sequence":"first","affiliation":[]},{"given":"Rasoul","family":"Ramezanian","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,11,17]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"D.Bridges andF.Richman.Varieties of Constructive Mathematics. London Math. Soc. Lecture Notes 97 (Cambridge University Press 1987).","DOI":"10.1017\/CBO9780511565663"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90029-3"},{"key":"e_1_2_1_4_2","unstructured":"S. C.Kleene andR. E.Vesley.The Foundations of Intuitionistic Mathematics Especially in Relation to Recursive Functions (North\u2010Holland 1965)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"D. A.Simovici andR. L.Tenney.Theory of Formal Languages with Applications (World Scientific Publishing Co. 1999).","DOI":"10.1142\/3991"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200410048"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2267043"},{"key":"e_1_2_1_8_2","unstructured":"A. S.Troelstra andD.van Dalen.Constructivism in Mathematics Vol. 1 (North\u2010Holland 1988)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200710094","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200710094","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200710094","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T19:32:54Z","timestamp":1699903974000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200710094"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,17]]},"references-count":7,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["10.1002\/malq.200710094"],"URL":"https:\/\/doi.org\/10.1002\/malq.200710094","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,17]]}}}