{“状态”:“确定”,“消息类型”:“工作”,“信息版本”:“1.0.0”,“邮件”:{“索引”:{-“日期-部件”:[[2022,3,30]],“日期-时间”:“2022-03-30T11:30:34Z”,“时间戳”:1648639834298},“参考-计数”:13,“出版商”:“剑桥大学出版社(CUP)”,“问题”:“4”,“许可证”:[{“开始”:{:“日期-零件”:[[2014,3,12]],“时间”:“2014-03-12T00:00:00Z”,“时间戳”:1394582400000},“content-version”:“unspecified”,“delay-in-days”:9598,“URL”:“https:\/\/www.cambridge.org\/core\/terms”}],“content-domain”:{“domain”(域):[],“crossmark-restriction”(交叉标记限制):false},”short-container-title“:[”J.symb.log.“],”published-print“:{”date-parts“:[[1987,12]}”,“abstract”(摘要):“图灵跳跃可以很容易地迭代任何有限的次数。挑战来自于超限迭代。a<\/jats:italic>(\u03c9<\/jats:italic>)<\/jax:sup>有一个直观的令人信服的定义:{\u2039m、 n<\/jats:italic>\u203a:n<\/jats:italic>\u2208a<\/jats:italic>(m<\/jats:italic>)<\/jax:sup>}。从Putnam等人[1]、[2]、[9]开始,到Jockusch-Simpson[8]和Hodes[6],最近的研究证明了这一点\u03c9<\/jats:italic>-跳转并扩展它。<\/jats:p>Jensen[3]、[7]的主代码非常有用。简单地说,a\u0394型n<\/jats:sub>(L(左)\u03b2<\/jats:sub><\/jax:italic>)-主代码是一个完整的\u0394型n<\/jats:sub>(L(左)\u03b2<\/jats:sub><\/jax:italic>)序号集,上确界尽可能小。与经典递归理论的联系很紧密。\u0394型n<\/jats:sub><\/jats:斜体>(L(左)\u03b2<\/jats:sub><\/jax:italic>)主代码是reals,它们是图灵等效代码。如果a是一个\u0394型n<\/jats:sub>(L(左)\u03b2<\/jats:sub><\/jax:italic>)MC,然后a\u2032<\/jats:italic>是一个\u0394<\/jats:italic>n<\/jats:italic>+1(L(左)\u03b2<\/jats:sub><\/jax:italic>)MC。直观地满足超限跳跃,例如\u03c9<\/jats:italic>-在上面跳转,生成一个与主代码的初始段相等的图灵跳转层次结构<\/jats:p>Hodes利用这些事实定义了0\u03b1<\/jats:italic><\/jax:sup>,\u03b1<\/jats:italic><,理论上设置为\u03b1<\/jats:italic>th MC是实数,然后证明0的跳跃理论定义的等价性\u03b1<\/jats:italic><\/jax:sup>。后继代码是它们的前一个代码的跳跃,对于一个极限\u03bb<\/jats:italic>,0\u03bb是与{0关联的一组度数中的最小值\u03b1<\/jats:italic>:\u03b1<\/jats:italic>:<\u03bb<\/jats:italic>}<\/jats:p>“,”DOI“:”10.2307\/2273829“,”type“:”journal-article“,”created“:{”date-parts“:[[2006,5,6]],”date-time“:”2006-05-06T22:23:41Z“,”timestamp“:1146954221000},”page“:52“,”作者“:[{”给定“:”罗伯特·S“,”family“:”Lubarsky“,”sequence“:”first“,”affiliation“:[]}],”member“:”56“,”published-online“:{”date-parts“:[[2014,3,12]},”reference“:[{”key“:”S0022481200029340_ref001“,”doi-asserted-by“:“,”doi“:”10.1090\/S0002-9947-1969-0242673-X“},{”键“:”S0022481200029340_ref013“,”doi-asserted-by“:”publisher“,”doi“:”10.1016\/0003-4843(78)90026-8“},{“key”:“S0022481 200029340_ ref002”,“first page”:”497“,”volume“:”33“,”author“:”Boolos“,”year“:”1968“,”journal-title“:”可构造整数集的不可解程度“}”,{”key“:ted-by“:”publisher“,”doi“:”10.1007 \/BF02761905“},{“key”:“S0022481200029340_ref007”,“首页”:“204”,”卷“:“45”,“作者”:“Hodes”,年:“1980”,“日记标题”:“跳转超限”},}“密钥”:“SO00224812000 29340_ref008”,‘doi-asserted-by’:“publisher”,《doi》:“10.1016\/0003-4843(72)90001-0”}200029340_ref009“,”doi-asserted-by“:”publisher“,”doi“:”10.1016\/0003-4843(76)90023-1“},{“key”:“S0022481200029340_ref010”,“doi-asserted-by”:“publisher”,”doi“:”10.1016\/S0049-237X(08)71236-9“}、{“key”:“SO022481200029.340_ref011”、“doi-sserted-by“:”publisher“,”doi:“10.1016\\0003-4843(74)90005-9”},“key“:”S0022481 200029340_ ref012“,”doi-asserted-by“:”publisher“,”doi“:”10.1090\/pspum\/013.1\/0276079“},{“key“:”S0022481200029340_ref005“,”doi-asserted-by“:”publisher“,“doi”:“10.2307\/1971132”},{“key”:“S0022481 200029340_ ref004”,“doi-assert-by”:“publisher”,”doi“:”10.1007\/BFb0059290“}],“container-title”:[“Journal of Symbolic Logic”],“original-title“:[],”language“:”en“,”link“:[{”URL“:”https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200029340“,“content-type”:“unspecified”,“content-version”:“vor”,“intended-application”:“similarity-checking”}],“deposed”:{“date-parts”:[[2019,5,20]],“date-time”:”2019-05-20T21:17:12Z“timestamp”:1558387032000},“score”:1,“resource”:{“primary”:{“URL”:“https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200029340\/type\/journal_article“}},“副标题”:[],“短标题”:[],“已发布”:{“日期部分”:[[1987,12]]},”references-count“:13,”journal-issue“:{”issue“:”4“,”published-print“:{”date-parts“:[[11987,12]}}”,“alternative-id”:[“S00224812000 29340“],”URL“:”http://\/dx.doi.org\/10.2307\/2273829“,”关系“:{},”ISSN“:[”0022-4812“,”1943-5886“],”ISSN-type“:[{”value“:”0022-5812“,“type”:“print”},{”value“:”1943-58“,”type“:”electronic“}],“subject”:[],“published”:{“date-parts”:[[1987,12]}}}}