{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T00:08:48Z","timestamp":1706659728239},"reference-count":24,"publisher":"Duke University Press","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Notre Dame J. Formal Logic"],"published-print":{"date-parts":[[2016,1,1]]},"DOI":"10.1215\/00294527-3489987","type":"journal-article","created":{"date-parts":[[2016,3,24]],"date-time":"2016-03-24T14:23:22Z","timestamp":1458829402000},"source":"Crossref","is-referenced-by-count":0,"title":["Some Remarks on Real Numbers Induced by First-Order Spectra"],"prefix":"10.1215","volume":"57","author":[{"given":"Sune Kristian","family":"Jakobsen","sequence":"first","affiliation":[]},{"given":"Jakob Grue","family":"Simonsen","sequence":"additional","affiliation":[]}],"member":"73","reference":[{"key":"8","doi-asserted-by":"publisher","unstructured":"[8] Durand, A., N. D. Jones, J. Makowsky, and M. More, \u201cFifty years of the spectrum problem: Survey and new results,\u201d preprint, <a href=\"arXiv:0907.5495v1\">arXiv:0907.5495v1<\/a> [math.LO].","DOI":"10.2178\/bsl.1804020"},{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] Adamczewski, B., and J. Cassaigne, \u201cDiophantine properties of real numbers generated by finite automata,\u201d <i>Compositio Mathematica<\/i>, vol. 142 (2006), pp. 1351\u201372.","DOI":"10.1112\/S0010437X06002247"},{"key":"2","doi-asserted-by":"crossref","unstructured":"[2] Allouche, J.-P., and J. Shallit, <i>Automatic Sequences: Theory, Applications, Generalizations<\/i>, Cambridge University Press, Cambridge, 2003.","DOI":"10.1017\/CBO9780511546563"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] B\u00e9al, M.-P., F. Mignosi, A. Restivo, and M. Sciortino, \u201cForbidden words in symbolic dynamics,\u201d <i>Advances in Applied Mathematics<\/i>, vol. 25 (2000), pp. 163\u201393.","DOI":"10.1006\/aama.2000.0682"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] Brouwer, L., \u201cBesitzt jede reelle Zahl eine Dezimalbruchentwicklung?\u201d <i>Mathematische Annalen<\/i>, vol. 83 (1921), pp. 201\u201310.","DOI":"10.1007\/BF01458382"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] Champernowne, D. G., \u201cThe construction of decimals normal in the scale of ten,\u201d <i>Journal of the London Mathematical Society (2)<\/i>, vol. S1-8 (1933), pp. 254\u201360.","DOI":"10.1112\/jlms\/s1-8.4.254"},{"key":"6","doi-asserted-by":"crossref","unstructured":"[6] Chomsky, N., and G. A. Miller, \u201cFinite state languages,\u201d <i>Information and Control<\/i>, vol. 1 (1958), pp. 91\u2013112.","DOI":"10.1016\/S0019-9958(58)90082-2"},{"key":"7","doi-asserted-by":"publisher","unstructured":"[7] Durand, A., N. D. Jones, J. Makowsky, and M. More, \u201cFifty years of the spectrum problem: Survey and new results,\u201d <i>Bulletin of Symbolic Logic<\/i>, vol. 18 (2012), pp. 505\u201353.","DOI":"10.2178\/bsl.1804020"},{"key":"9","doi-asserted-by":"crossref","unstructured":"[9] Ebbinghaus, H.-D., J. Flum, and W. Thomas, <i>Mathematical Logic<\/i>, 2nd ed., <i>Undergraduate Texts in Mathematics<\/i>, Springer, New York, 1994.","DOI":"10.1007\/978-1-4757-2355-7"},{"key":"10","doi-asserted-by":"crossref","unstructured":"[10] Enderton, H. B., <i>A Mathematical Introduction to Logic<\/i>, 2nd ed., Harcourt\/Academic Press, Burlington, Mass., 2001.","DOI":"10.1016\/B978-0-08-049646-7.50005-9"},{"key":"11","unstructured":"[11] Hardy, G. H, and E. M. Wright, <i>An Introduction to the Theory of Numbers<\/i>, Oxford University Press, Oxford, 1938."},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] Hartmanis, J., and R. E. Stearns, \u201cOn the computational complexity of algorithms,\u201d <i>Transactions of the American Mathematical Society<\/i>, vol. 117 (1965), pp. 285\u2013306.","DOI":"10.1090\/S0002-9947-1965-0170805-7"},{"key":"13","unstructured":"[13] Hertling, P., and C. Spandl, \u201cShifts with decidable language and non-computable entropy,\u201d <i>Discrete Mathematics and Theoretical Computer Science<\/i>, vol. 10 (2008), pp. 75\u201393."},{"key":"14","doi-asserted-by":"crossref","unstructured":"[14] Jones, N. D., <i>Computability and Complexity from a Programming Perspective<\/i>, Foundations of Computing, MIT Press, 1997.","DOI":"10.7551\/mitpress\/2003.001.0001"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] Jones, N. D., and A. L. Selman, \u201cTuring machines and the spectra of first-order formulas,\u201d <i>Journal of Symbolic Logic<\/i>, vol. 39 (1974), pp. 139\u201350.","DOI":"10.2307\/2272354"},{"key":"16","unstructured":"[16] J\u00fcrgensen, H., H.-J. Shyr, and G. Thierrin, \u201cDisjunctive $\\omega$-languages,\u201d <i>Elektronische Informationsverarbeitung und Kybernetik<\/i>, vol. 19 (1983), pp. 267\u201378."},{"key":"17","doi-asserted-by":"publisher","unstructured":"[17] J\u00fcrgensen, H., and G. Thierrin, \u201cOn $\\omega$-languages whose syntactic monoid is trivial,\u201d <i>International Journal of Computer and Information Sciences<\/i>, vol. 12 (1983), pp. 359\u201365.","DOI":"10.1007\/BF01008047"},{"key":"18","doi-asserted-by":"crossref","unstructured":"[18] Ko, K.-I., <i>Complexity Theory of Real Functions<\/i>, Birkh\u00e4user, Boston, 1991.","DOI":"10.1007\/978-1-4684-6802-1"},{"key":"19","doi-asserted-by":"crossref","unstructured":"[19] Lind, D., and B. Marcus, <i>An Introduction to Symbolic Dynamics and Coding<\/i>, Cambridge University Press, Cambridge, 1995.","DOI":"10.1017\/CBO9780511626302"},{"key":"20","unstructured":"[20] Papadimitriou, C. H., <i>Computational Complexity<\/i>, Addison-Wesley, Reading, Mass., 1994."},{"key":"21","doi-asserted-by":"crossref","unstructured":"[21] Sipser, M., <i>Introduction to the Theory of Computation<\/i>, PWS Publishing Company, 1996.","DOI":"10.1145\/230514.571645"},{"key":"22","doi-asserted-by":"crossref","unstructured":"[22] Turing, A., \u201cOn computable numbers, with an application to the Entscheidungsproblem: A correction,\u201d <i>Proceedings of the London Mathematical Society<\/i>, vol. 43 (1937), pp. 544\u201346.","DOI":"10.1112\/plms\/s2-43.6.544"},{"key":"23","unstructured":"[23] Weihrauch, K., <i>Computable Analysis: An Introduction<\/i>, Springer, Berlin, 1998."},{"key":"24","doi-asserted-by":"publisher","unstructured":"[24] Zheng, X., and K. Weihrauch, \u201cThe arithmetical hierarchy of real numbers,\u201d <i>Mathematical Logic Quarterly<\/i>, vol. 47 (2001), pp. 51\u201365.","DOI":"10.1002\/1521-3870(200101)47:1<51::AID-MALQ51>3.0.CO;2-W"}],"container-title":["Notre Dame Journal of Formal Logic"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/journalArticle\/Download?urlid=10.1215\/00294527-3489987","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T20:58:42Z","timestamp":1706648322000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/notre-dame-journal-of-formal-logic\/volume-57\/issue-3\/Some-Remarks-on-Real-Numbers-Induced-by-First-Order-Spectra\/10.1215\/00294527-3489987.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,1]]},"references-count":24,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,1,1]]}},"URL":"https:\/\/doi.org\/10.1215\/00294527-3489987","relation":{},"ISSN":["0029-4527"],"issn-type":[{"value":"0029-4527","type":"print"}],"subject":[],"published":{"date-parts":[[2016,1,1]]}}}