{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T00:18:02Z","timestamp":1706660282277},"reference-count":15,"publisher":"Duke University Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Notre Dame J. Formal Logic"],"published-print":{"date-parts":[[2020,1,1]]},"DOI":"10.1215\/00294527-2019-0037","type":"journal-article","created":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T03:01:11Z","timestamp":1576810871000},"source":"Crossref","is-referenced-by-count":0,"title":["The Logic of Turing Progressions"],"prefix":"10.1215","volume":"61","author":[{"given":"Eduardo","family":"Hermo Reyes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joost J.","family":"Joosten","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"73","reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] Beklemishev, L. D., \u201cProvability logics for natural Turing progressions of arithmetical theories,\u201d <i>Studia Logica<\/i>, vol. 50 (1991), pp. 107\u201328.","DOI":"10.1007\/BF00370390"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] Beklemishev, L. D., \u201cIterated local reflection versus iterated consistency,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 75 (1995), pp. 25\u201348.","DOI":"10.1016\/0168-0072(95)00007-4"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] Beklemishev, L. D., \u201cProof-theoretic analysis by iterated reflection,\u201d <i>Archive for Mathematical Logic<\/i>, vol. 42 (2003), pp. 515\u201352.","DOI":"10.1007\/s00153-002-0158-7"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] Beklemishev, L. D., \u201cProvability algebras and proof-theoretic ordinals, I,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 128 (2004), pp. 103\u201323.","DOI":"10.1016\/j.apal.2003.11.030"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] Beklemishev, L. D., \u201cReflection schemes and provability algebras in formal arithmetic,\u201d <i>Russian Mathematical Surveys<\/i>, vol. 60 (2005), pp. 197\u2013268.","DOI":"10.1070\/RM2005v060n02ABEH000823"},{"key":"6","unstructured":"[6] Beklemishev, L. D., \u201cCalibrating provability logic: From modal logic to reflection calculus,\u201d pp. 89\u201394 in <i>Proceedings of the 9th Conference (AiML 2012) (Copenhagen, 2012)<\/i>, edited by T. Bolander, T. Bra\u00fcner, S. Ghilardi, and L. Moss, vol. 9 of <i>Advances in Modal Logic<\/i>, College Publications, London, 2012."},{"key":"7","doi-asserted-by":"publisher","unstructured":"[7] Beklemishev, L. D., \u201cPositive provability logic for uniform reflection principles,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 165 (2014), pp. 82\u2013105.","DOI":"10.1016\/j.apal.2013.07.006"},{"key":"8","doi-asserted-by":"publisher","unstructured":"[8] Dashkov, E. V., \u201cOn the positive fragment of the polymodal provability logic GLP,\u201d <i>Mathematical Notes<\/i>, vol. 91 (2012), pp. 318\u201333.","DOI":"10.1134\/S0001434612030029"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[9] Fern\u00e1ndez-Duque, D., and J. J. Joosten, \u201cHyperations, Veblen progressions and transfinite iteration of ordinal functions,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 164 (2013), pp. 785\u2013801.","DOI":"10.1016\/j.apal.2013.01.002"},{"key":"10","doi-asserted-by":"crossref","unstructured":"[10] G\u00f6del, K., \u201c\u00dcber formal unentscheidbare S\u00e4tze der Principia Mathematica und verwandter Systeme, I,\u201d <i>Monatshefte f\u00fcr Mathematik und Physik<\/i>, vol. 38 (1931), pp. 173\u201398.","DOI":"10.1007\/BF01700692"},{"key":"11","unstructured":"[11] Hermo Reyes, E., and J. J. Joosten, \u201cRelational semantics for the Turing Schmerl calculus,\u201d pp. 327\u201346 in <i>Proceedings of the Twelfth Conference (AiML 2018) (Bern, 2018)<\/i>, edited by G. Bezhanishvili, G. D\u2019Agostino, G. Metcalfe, and T. Studer, vol. 12 of <i>Advances in Modal Logic<\/i>, College Publications, London, 2018."},{"key":"12","unstructured":"[12] Japaridze, G., \u201cThe polymodal provability logic\u201d (in Russian), pp. 16\u201348 in <i>Intensional Logics and Logical Structure of Theories (Telavi, 1985)<\/i>, Mecniereba, Tbilisi, 1988."},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] Joosten, J. J., \u201cTuring-Taylor expansions for arithmetic theories,\u201d <i>Studia Logica<\/i>, vol. 104 (2016), pp. 1225\u201343.","DOI":"10.1007\/s11225-016-9674-z"},{"key":"14","doi-asserted-by":"crossref","unstructured":"[14] Schmerl, U. R., \u201cA fine structure generated by reflection formulas over primitive recursive arithmetic,\u201d pp. 335\u201350 in <i>Logic Colloquium \u201978 (Mons, 1978)<\/i>, edited by M. Boffa, D. Dalen, and K. McAloon, vol. 97 of <i>Studies in Logic and the Foundations of Mathematics<\/i>, North-Holland, New York, 1979.","DOI":"10.1016\/S0049-237X(08)71633-1"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] Turing, A. M., \u201cSystems of logic based on ordinals,\u201d <i>Proceedings of the London Mathematical Society (2)<\/i>, vol. 45 (1939), pp. 161\u2013228.","DOI":"10.1112\/plms\/s2-45.1.161"}],"container-title":["Notre Dame Journal of Formal Logic"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/journalArticle\/Download?urlid=10.1215\/00294527-2019-0037","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T21:00:05Z","timestamp":1706648405000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/notre-dame-journal-of-formal-logic\/volume-61\/issue-1\/The-Logic-of-Turing-Progressions\/10.1215\/00294527-2019-0037.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,1]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,1]]}},"URL":"https:\/\/doi.org\/10.1215\/00294527-2019-0037","relation":{},"ISSN":["0029-4527"],"issn-type":[{"value":"0029-4527","type":"print"}],"subject":[],"published":{"date-parts":[[2020,1,1]]}}}