{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T05:30:33Z","timestamp":1757568633724},"reference-count":19,"publisher":"Duke University Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Notre Dame J. Formal Logic"],"published-print":{"date-parts":[[2006,1,1]]},"DOI":"10.1305\/ndjfl\/1143468312","type":"journal-article","created":{"date-parts":[[2006,3,28]],"date-time":"2006-03-28T08:08:43Z","timestamp":1143533323000},"source":"Crossref","is-referenced-by-count":10,"title":["Constructive Logic and the Medvedev Lattice"],"prefix":"10.1215","volume":"47","author":[{"given":"Sebastiaan A.","family":"Terwijn","sequence":"first","affiliation":[]}],"member":"73","reference":[{"key":"2","doi-asserted-by":"crossref","unstructured":"[2] Dyment, E. Z., \"Certain properties of the Medvedev lattice\", <i>Mathematics of the USSR Sbornik<\/i>, vol. 30 (1976), pp. 321--40.","DOI":"10.1070\/SM1976v030n03ABEH002277"},{"key":"3","unstructured":"[3] Jankov, V. A., \"Calculus of the weak law of the excluded middle\", <i>Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya<\/i>, vol. 32 (1968), pp. 1044--51. In Russian."},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] Jockusch, C. G., Jr., and M. S. Paterson, \"Completely autoreducible degrees\", <i>Zeitschrift f\u00fcr mathematische Logik und Grundlagen der Mathematik<\/i>, vol. 22 (1976), pp. 571--75.","DOI":"10.1002\/malq.19760220164"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] Kolmogoroff, A., \"Zur Deutung der intuitionistischen Logik\", <i>Mathematische Zeitschrift<\/i>, vol. 35 (1932), pp. 58--65.","DOI":"10.1007\/BF01186549"},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] Lachlan, A. H., and R. Lebeuf, \"Countable initial segments of the degrees of unsolvability\", <i>The Journal of Symbolic Logic<\/i>, vol. 41 (1976), pp. 289--300.","DOI":"10.2307\/2272227"},{"key":"7","unstructured":"[7] Lerman, M., <i>Degrees of Unsolvability. Local and Global Theory<\/i>, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1983."},{"key":"8","unstructured":"[8] Medvedev, Y. T., \"Degrees of difficulty of the mass problem\", <i>Doklady Akademii Nauk SSSR<\/i>, vol. 104 (1955), pp. 501--504."},{"key":"9","unstructured":"[9] Medvedev, Y. T., \"Finite problems\", <i>Doklady Akademii Nauk SSSR<\/i>, vol. 142 (1962), pp. 1015--1018."},{"key":"11","unstructured":"[11] Odifreddi, P., <i>Classical Recursion Theory. The Theory of Functions and Sets of Natural Numbers<\/i>, vol. 125 of <i>Studies in Logic and the Foundations of Mathematics<\/i>, North-Holland Publishing Co., Amsterdam, 1989."},{"key":"12","unstructured":"[12] Rogers, H., Jr., <i>Theory of Recursive Functions and Effective Computability<\/i>, McGraw-Hill Book Co., New York, 1967."},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] Shen, A., and N. Vereshchagin, \"Logical operations and Kolmogorov complexity\", <i>Theoretical Computer Science<\/i>, vol. 271 (2002), pp. 125--29. Electronic Colloquium on Computational Complexity, report TR01-088, 2001.","DOI":"10.1016\/S0304-3975(01)00035-4"},{"key":"14","doi-asserted-by":"crossref","unstructured":"[14] Skvortsova, E. Z., \"A faithful interpretation of the intuitionistic propositional calculus by means of an initial segment of the Medvedev lattice\", <i>Sibirski\u012d Matematicheski\u012d Zhurnal<\/i>, vol. 29 (1988), pp. 133--39. In Russian.","DOI":"10.1007\/BF00975025"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] Sorbi, A., \"Some remarks on the algebraic structure of the Medvedev lattice\", <i>The Journal of Symbolic Logic<\/i>, vol. 55 (1990), pp. 831--53.","DOI":"10.2307\/2274668"},{"key":"16","doi-asserted-by":"publisher","unstructured":"[16] Sorbi, A., \"Embedding Brouwer algebras in the Medvedev lattice\", <i>Notre Dame Journal of Formal Logic<\/i>, vol. 32 (1991), pp. 266--75.","DOI":"10.1305\/ndjfl\/1093635751"},{"key":"17","doi-asserted-by":"publisher","unstructured":"[17] Sorbi, A., \"Some quotient lattices of the Medvedev lattice\", <i>Zeitschrift f\u00fcr mathematische Logik und Grundlagen der Mathematik<\/i>, vol. 37 (1991), pp. 167--82.","DOI":"10.1002\/malq.19910370905"},{"key":"18","doi-asserted-by":"crossref","unstructured":"[18] Sorbi, A., \"The Medvedev lattice of degrees of difficulty\", pp. 289--312 in <i>Computability, Enumerability, Unsolvability: Directions in Recursion Theory<\/i>, edited by S. B. Cooper, T. A. Slaman, and S. S. Wainer, vol. 224 of <i>London Mathematical Society Lecture Notes<\/i>, Cambridge University Press, Cambridge, 1996.","DOI":"10.1017\/CBO9780511629167.015"},{"key":"1","unstructured":"[1] Balbes, R., and P. Dwinger, <i>Distributive Lattices<\/i>, University of Missouri Press, Columbia, 1974."},{"key":"10","unstructured":"[10] Muchnik, A. A., \"On strong and weak reducibility of algorithmic problems\", <i>Sibirski\u012d Matematicheski\u012d Zhurnal<\/i>, vol. 4 (1963), pp. 1328--41. In Russian."},{"key":"19","doi-asserted-by":"publisher","unstructured":"[19] Terwijn, S. A., \"The Medvedev lattice of computably closed sets\". <i>Archive for Mathematical Logic<\/i>, vol. 45 (2006), pp. 179--90.","DOI":"10.1007\/s00153-005-0278-y"}],"container-title":["Notre Dame Journal of Formal Logic"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/journalArticle\/Download?urlid=10.1305\/ndjfl\/1143468312","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T20:56:34Z","timestamp":1706648194000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/notre-dame-journal-of-formal-logic\/volume-47\/issue-1\/Constructive-Logic-and-the-Medvedev-Lattice\/10.1305\/ndjfl\/1143468312.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1,1]]},"references-count":19,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,1]]}},"URL":"https:\/\/doi.org\/10.1305\/ndjfl\/1143468312","relation":{},"ISSN":["0029-4527"],"issn-type":[{"value":"0029-4527","type":"print"}],"subject":[],"published":{"date-parts":[[2006,1,1]]}}}