{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T02:56:32Z","timestamp":1764212192447,"version":"3.37.3"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2021,4,15]],"date-time":"2021-04-15T00:00:00Z","timestamp":1618444800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,15]],"date-time":"2021-04-15T00:00:00Z","timestamp":1618444800000},"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":["Stud Logica"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s11225-021-09945-2","type":"journal-article","created":{"date-parts":[[2021,4,15]],"date-time":"2021-04-15T17:04:03Z","timestamp":1618506243000},"page":"1159-1169","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Incompleteness and the Halting Problem"],"prefix":"10.1007","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8711-6799","authenticated-orcid":false,"given":"Cristian S.","family":"Calude","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,15]]},"reference":[{"key":"9945_CR1","unstructured":"Avigad, J., Computability and Incompleteness-Lectures Notes, https:\/\/www.andrew.cmu.edu\/user\/avigad\/Teaching\/candinotes.pdf, 2007."},{"key":"9945_CR2","doi-asserted-by":"crossref","unstructured":"Calude, C., Information and Randomness\u2014An Algorithmic Perspective, 2nd ed., Springer, Berlin, 2002.","DOI":"10.1007\/978-3-662-04978-5"},{"key":"9945_CR3","doi-asserted-by":"crossref","unstructured":"Calude, C., and G. P\u0103un, Independent instances for some undecidable problems, RAIRO-Theoretical Informatics and Applications-Informatique Th\u00e9orique et Applications 17(1):49\u201354, 1983.","DOI":"10.1051\/ita\/1983170100491"},{"key":"9945_CR4","unstructured":"Calude, C. S., and S. Rudeanu, Proving as a computable procedure, Fundamenta Informaticae 64(1\u20134):43\u201352, 2005."},{"key":"9945_CR5","doi-asserted-by":"crossref","unstructured":"Chaitin, G. J., Computational complexity and G\u00f6del\u2019s incompleteness theorem, ACM SIGACT News 9:11\u201312, 1971.","DOI":"10.1145\/1247066.1247068"},{"key":"9945_CR6","doi-asserted-by":"publisher","DOI":"10.1142\/1861","volume-title":"Information-Theoretic Incompleteness","author":"Gregory J Chaitin","year":"1992","unstructured":"Chaitin, G. J., Information-Theoretic Incompleteness, World Scientific, Singapore, 1992."},{"key":"9945_CR7","unstructured":"Copeland, B.\u00a0J., (ed.), The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, and Artificial Life plus The Secrets of Enigma, Oxford University Press, Oxford, 2004."},{"key":"9945_CR8","unstructured":"Davis, M., Here There Be Monsters, Presentation at Courant Institute, NYU."},{"key":"9945_CR9","volume-title":"Computability and Unsolvability","author":"Martin Davis","year":"1958","unstructured":"Davis, M., Computability and Unsolvability, McGraw-Hill, New York, 1958."},{"key":"9945_CR10","first-page":"89","volume-title":"Randomness and Complexity","author":"Martin Davis","year":"2007","unstructured":"Davis, M., What is a computation?, in C. S. Calude, Randomness and Complexity. From Leibniz to Chaitin, World Scientific Publishing, Singapore, 2007, pp. 89\u2013113."},{"key":"9945_CR11","volume-title":"The Universal Computer: the Road from Leibniz to Turing","author":"Martin Davis","year":"2017","unstructured":"Davis, M., The Universal Computer: the Road from Leibniz to Turing, W. W. Norton Company, New York, 2017."},{"key":"9945_CR12","unstructured":"G\u00f6del, K., \u00dcber die Vollst\u00e4ndigkeit des Logikkalk\u00fcls, Ph.D. thesis, University of Vienna, 1929."},{"key":"9945_CR13","doi-asserted-by":"crossref","unstructured":"G\u00f6del, K., Uber formal unentscheidbare S\u00e4tze der Principia Mathematica und verwandter Systeme I, Monatshefte f\u00fcr Mathematik 38:173\u2013198, 1931.","DOI":"10.1007\/BF01700692"},{"key":"9945_CR14","first-page":"71","volume-title":"The Undecidable","author":"Kurt G\u00f6del","year":"1965","unstructured":"G\u00f6del, K., Postscriptum, in M. Davis, (ed.), The Undecidable. Basic Papers on Undecidable, Unsolvable Problems and Computable Functions, Raven Press, Hewlett, N.Y., 1965, pp. 71\u201372."},{"key":"9945_CR15","unstructured":"Hintikka, J., On G\u00f6del, Wadsworth, 2000."},{"key":"9945_CR16","volume-title":"Introduction to Metamathematics","author":"Stephen C Kleene","year":"1952","unstructured":"Kleene, S.\u00a0C., Introduction to Metamathematics, North-Holland, Amsterdam, 1952."},{"key":"9945_CR17","unstructured":"Kritchman, S., and R. Raz, The surprise examination paradox and the second incompleteness theorem, Notices of the AMS 57(11):1454\u20131458, 2010."},{"key":"9945_CR18","doi-asserted-by":"crossref","unstructured":"Longo, G., Interfaces of incompleteness, in G. Minati, M. R. Abram, and E. Pessa, (eds.), Systemics of Incompleteness and Quasi-Systems, Springer Nature, 2019, pp. 3\u201355.","DOI":"10.1007\/978-3-030-15277-2_1"},{"key":"9945_CR19","doi-asserted-by":"crossref","unstructured":"Murawski, R., Undefinability of truth. the problem of the priority: Tarski vs. G\u00f6del, History and Philosophy of Logic 19:153\u2013160, 1998.","DOI":"10.1080\/01445349808837306"},{"key":"9945_CR20","doi-asserted-by":"crossref","unstructured":"Post, E. L., Introduction to a general theory of elementary propositions, American Journal of Mathematics 43(3):163\u2013185, 1921.","DOI":"10.2307\/2370324"},{"key":"9945_CR21","unstructured":"Sipser, M., Introduction to the Theory of Computation, 3rd ed., Cengage Learning, 2013."},{"key":"9945_CR22","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139149105","volume-title":"An Introduction to G\u00f6del\u2019s Theorems","author":"P Smith","year":"2013","unstructured":"Smith, P., An Introduction to G\u00f6del\u2019s Theorems, Cambridge University Press, Cambridge, UK, 2013."},{"key":"9945_CR23","unstructured":"Tarski, A., Poj\u0119scie prawdy w j\u0119zykach nauk dedukcyjnych, Towarzystwo Naukowe Warszawskie, Warszawa, 1933."}],"container-title":["Studia Logica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-021-09945-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11225-021-09945-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-021-09945-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T12:35:17Z","timestamp":1724848517000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11225-021-09945-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,15]]},"references-count":23,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["9945"],"URL":"https:\/\/doi.org\/10.1007\/s11225-021-09945-2","relation":{},"ISSN":["0039-3215","1572-8730"],"issn-type":[{"type":"print","value":"0039-3215"},{"type":"electronic","value":"1572-8730"}],"subject":[],"published":{"date-parts":[[2021,4,15]]},"assertion":[{"value":"18 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 April 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}