{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T15:54:29Z","timestamp":1694793269131},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2005,11,10]],"date-time":"2005-11-10T00:00:00Z","timestamp":1131580800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2005,11,10]],"date-time":"2005-11-10T00:00:00Z","timestamp":1131580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2006,5]]},"DOI":"10.1007\/s00153-005-0319-6","type":"journal-article","created":{"date-parts":[[2005,11,10]],"date-time":"2005-11-10T11:14:15Z","timestamp":1131621255000},"page":"393-410","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Small \u03a00\n                     1 Classes"],"prefix":"10.1007","volume":"45","author":[{"given":"Stephen","family":"Binns","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2005,11,10]]},"reference":[{"key":"319_CR1","doi-asserted-by":"crossref","unstructured":"Ambos-Spies, K., M\u00fcller, G.H., Sacks, G.E. (eds.): editors. Recursion Theory Week. Number 1432 in Lecture Notes in Mathematics. Springer-Verlag, 1990. IX + 393 pages","DOI":"10.1007\/BFb0086109"},{"key":"319_CR2","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s00153-003-0195-x","volume":"43","author":"Binns","year":"2004","unstructured":"Binns, S., Simpson, S.G.: Embeddings into the Medvedev and Muchnik lattices of \u03a00\n                           1 classes. Arch. Math. Logic 43, 399\u2013414 (2004)","journal-title":"Arch. Math. Logic"},{"key":"319_CR3","unstructured":"Binns, S.E.: The Medvedev and Muchnik Lattices of \u03a01\n                           0 classes. PhD thesis, The Pennsylvania State University, 2003. 80 pages"},{"key":"319_CR4","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1002\/malq.200310034","volume":"49","author":"Binns","year":"2003","unstructured":"Binns, S.E.: A splitting theorem for the Medvedev and Muchnik lattices. Math. Logic Quarterly 49, 327\u2013335 July (2003)","journal-title":"Math. Logic Quarterly"},{"key":"319_CR5","unstructured":"Cenzer, D., Hinman, P.G.: Density of the Medvedev lattice of \u03a00\n                           1 classes. Archive for Mathematical Logic, March 2003. Online First Publication, DOI 10.1007\/s00153-002-0166-7"},{"key":"319_CR6","doi-asserted-by":"publisher","first-page":"4899","DOI":"10.1090\/S0002-9947-01-02821-5","volume":"353","author":"Cholak","year":"12","unstructured":"Cholak, P., Coles, R., Downey, R, Herrmann. E.: Automorphisms of the lattice of \u03a00\n                           1 classes; perfect thin classes and ANC degrees. Transactions of the American Mathematical Society 353 (12), 4899\u20134924 (2001)","journal-title":"Transactions of the American Mathematical Society"},{"key":"319_CR7","doi-asserted-by":"crossref","unstructured":"Cooper, S.B., Slaman, T.A., Wainer, S.S. (eds.): Computability, Enumerability, Unsolvability: Directions in Recursion Theory. Number 224 in London Mathematical Society Lecture Notes. Cambridge University Press, 1996. VII + 347 pages","DOI":"10.1017\/CBO9780511629167"},{"key":"319_CR8","doi-asserted-by":"crossref","unstructured":"Downey, R.G., Jockusch, C.G. Jr., Stob, M.: Array nonrecursive sets and multiple permitting arguments. In: [1], 1990, pp. 141\u2013174","DOI":"10.1007\/BFb0086116"},{"key":"319_CR9","doi-asserted-by":"crossref","unstructured":"Downey, R.G., Jockusch, C.G. Jr., Stob, M.: Array nonrecursive degrees and genericity. In [7], 1996, pp. 93\u2013105","DOI":"10.1017\/CBO9780511629167.005"},{"key":"319_CR10","doi-asserted-by":"publisher","first-page":"35","DOI":"10.2307\/1996261","volume":"173","author":"Jockusch","year":"1972","unstructured":"Jockusch, C.G. Jr., Soare, R.I.: \u03a00\n                           1 classes and degrees of theories. Transactions of the American Mathematical Society 173, 35\u201356 (1972)","journal-title":"Transactions of the American Mathematical Society"},{"key":"319_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/1994768","volume":"130","author":"Lachlan","year":"1968","unstructured":"Lachlan, A.H.: On the lattice of recursively enumerable sets. Transactions of the American Math. Soc. 130, 1\u201327 (1968)","journal-title":"Transactions of the American Math. Soc."},{"key":"319_CR12","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1002\/malq.19660120125","volume":"12","author":"D.A. Martin","year":"1966","unstructured":"Martin, D.A., Classes of recursively enumerable sets and degrees of unsolvability. Zeitschrift f\u00fcr Mathematische Logik und Grundlagen der Mathematik 12, 295\u2013310 (1966)","journal-title":"Zeitschrift f\u00fcr Mathematische Logik und Grundlagen der Mathematik"},{"key":"319_CR13","unstructured":"Odifreddi, P.: Classical Recursion Theory, volume 1. 1950. xvii+ 668 pages"},{"key":"319_CR14","doi-asserted-by":"crossref","unstructured":"Ohashi, K.: A stronger form of a theorem of Friedberg. Notre Dame Journal of Formal Logic, Vol. V, Num. 1:10\u201312, Jan. 1964","DOI":"10.1305\/ndjfl\/1093957732"},{"key":"319_CR15","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1090\/S0002-9904-1944-08111-1","volume":"50","author":"Post","year":"1944","unstructured":"Post, E.: Recursively enumerable sets of positive integers and their decision problems. Bulletin of the American Mathematical Society 50, 284\u2013316 (1944)","journal-title":"Bulletin of the American Mathematical Society"},{"key":"319_CR16","doi-asserted-by":"publisher","first-page":"162","DOI":"10.2307\/2271653","volume":"32","author":"Robinson","year":"1967","unstructured":"Robinson, R.W.: Simplicity of recursively enumerable sets. J. Symbolic Logic 32, 162\u2013172 (1967)","journal-title":"J. Symbolic Logic"},{"key":"319_CR17","unstructured":"Rogers, H. Jr.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, 1967. XIX + 482 pages"},{"key":"319_CR18","unstructured":"Simpson, S.G. (ed.): Reverse Mathematics 2001. To appear"},{"key":"319_CR19","unstructured":"Simpson, S.G.: \u03a00\n                           1 sets and models of \n                  \n                . In [18]. Preprint, April 2000, 28 pages, to appear"},{"key":"319_CR20","doi-asserted-by":"crossref","unstructured":"Soare, R.I.: Recursively Enumerable Sets and Degrees. Perspectives in Mathematical Logic. Springer-Verlag, 1987. XVIII + 437 pages","DOI":"10.1007\/978-3-662-02460-7"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-005-0319-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-005-0319-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-005-0319-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-005-0319-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T00:04:38Z","timestamp":1652486678000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-005-0319-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11,10]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,5]]}},"alternative-id":["319"],"URL":"https:\/\/doi.org\/10.1007\/s00153-005-0319-6","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,11,10]]},"assertion":[{"value":"3 May 2004","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 August 2004","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 November 2005","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}