{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T16:43:43Z","timestamp":1743093823344,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662595329"},{"type":"electronic","value":"9783662595336"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-662-59533-6_12","type":"book-chapter","created":{"date-parts":[[2019,6,22]],"date-time":"2019-06-22T19:02:35Z","timestamp":1561230155000},"page":"195-207","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Self-contained Provability Calculus for $$\\varGamma _0$$"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8604-4183","authenticated-orcid":false,"given":"David","family":"Fern\u00e1ndez-Duque","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8982-6030","authenticated-orcid":false,"given":"Eduardo","family":"Hermo-Reyes","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,6,9]]},"reference":[{"key":"12_CR1","unstructured":"de Almeida Borges, A., Joosten, J.: The worm calculus. In: Bezhanishvili, G., D\u2019Agostino, G., Metcalfe, G., Studer, T. (eds.) Advances in Modal Logic, vol. 12. College Publications (2018)"},{"key":"12_CR2","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.apal.2003.11.030","volume":"128","author":"LD Beklemishev","year":"2004","unstructured":"Beklemishev, L.D.: Provability algebras and proof-theoretic ordinals, I. Ann. Pure Appl. Log. 128, 103\u2013124 (2004)","journal-title":"Ann. Pure Appl. Log."},{"key":"12_CR3","unstructured":"Beklemishev, L.D.: Veblen hierarchy in the context of provability algebras. In: H\u00e1jek, P., Vald\u00e9s-Villanueva, L., Westerst\u00e5hl, D. (eds.) Logic, Methodology and Philosophy of Science, Proceedings of the Twelfth International Congress, pp. 65\u201378. Kings College Publications (2005)"},{"key":"12_CR4","first-page":"89","volume-title":"Advances in Modal Logic","author":"LD Beklemishev","year":"2012","unstructured":"Beklemishev, L.D.: Calibrating provability logic. In: Bolander, T., Bra\u00fcner, T., Ghilardi, T.S., Moss, L. (eds.) Advances in Modal Logic, vol. 9, pp. 89\u201394. College Publications, London (2012)"},{"issue":"1","key":"12_CR5","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.apal.2013.07.006","volume":"165","author":"LD Beklemishev","year":"2014","unstructured":"Beklemishev, L.D.: Positive provability logic for uniform reflection principles. Ann. Pure Appl. Log. 165(1), 82\u2013105 (2014)","journal-title":"Ann. Pure Appl. Log."},{"issue":"3","key":"12_CR6","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/s11225-013-9490-7","volume":"102","author":"LD Beklemishev","year":"2014","unstructured":"Beklemishev, L.D., Fern\u00e1ndez-Duque, D., Joosten, J.J.: On provability logics with linearly ordered modalities. Stud. Log. 102(3), 541\u2013566 (2014)","journal-title":"Stud. Log."},{"issue":"12","key":"12_CR7","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1016\/j.apal.2013.06.008","volume":"164","author":"LD Beklemishev","year":"2013","unstructured":"Beklemishev, L.D., Gabelaia, D.: Topological completeness of the provabilitylogic GLP. Ann. Pure Appl. Log. 164(12), 1201\u20131223 (2013)","journal-title":"Ann. Pure Appl. Log."},{"issue":"4","key":"12_CR8","first-page":"534","volume":"7","author":"L Beklemishev","year":"2001","unstructured":"Beklemishev, L.: Another pathological well-ordering. Bull. Symb. Log. 7(4), 534\u2013534 (2001)","journal-title":"Bull. Symb. Log."},{"key":"12_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/978-3-662-55386-2_4","volume-title":"Logic, Language, Information, and Computation","author":"LD Beklemishev","year":"2017","unstructured":"Beklemishev, L.D.: On the reflection calculus with partial conservativity operators. In: Kennedy, J., de Queiroz, R.J.G.B. (eds.) WoLLIC 2017. LNCS, vol. 10388, pp. 48\u201367. Springer, Heidelberg (2017). \nhttps:\/\/doi.org\/10.1007\/978-3-662-55386-2_4"},{"issue":"4","key":"12_CR10","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1070\/RM9843","volume":"73","author":"L Beklemishev","year":"2018","unstructured":"Beklemishev, L.: Reflection calculus and conservativity spectra. Russ. Math. Surv. 73(4), 569\u2013613 (2018)","journal-title":"Russ. Math. Surv."},{"key":"12_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/978-3-319-72056-2_6","volume-title":"Logical Foundations of Computer Science","author":"LD Beklemishev","year":"2018","unstructured":"Beklemishev, L.D.: A universal algebra for the variable-free fragment of $${\\rm RC^\\nabla }$$. In: Artemov, S., Nerode, A. (eds.) LFCS 2018. LNCS, vol. 10703, pp. 91\u2013106. Springer, Cham (2018). \nhttps:\/\/doi.org\/10.1007\/978-3-319-72056-2_6"},{"key":"12_CR12","volume-title":"The Logic of Provability","author":"GS Boolos","year":"1993","unstructured":"Boolos, G.S.: The Logic of Provability. Cambridge University Press, Cambridge (1993)"},{"issue":"3\u20134","key":"12_CR13","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1134\/S0001434612030029","volume":"91","author":"EV Dashkov","year":"2012","unstructured":"Dashkov, E.V.: On the positive fragment of the polymodal provability logicGLP. Math. Notes 91(3\u20134), 318\u2013333 (2012)","journal-title":"Math. Notes"},{"issue":"3\u20134","key":"12_CR14","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s00153-014-0371-1","volume":"53","author":"D Fern\u00e1ndez-Duque","year":"2014","unstructured":"Fern\u00e1ndez-Duque, D.: The polytopologies of transfinite provability logic. Arch. Math. Log. 53(3\u20134), 385\u2013431 (2014)","journal-title":"Arch. Math. Log."},{"issue":"10","key":"12_CR15","first-page":"3277","volume":"4","author":"D F\u00e9rnandez-Duque","year":"2017","unstructured":"F\u00e9rnandez-Duque, D.: Worms and spiders: reflection calculi and ordinal notation systems. J. Appl. Log. - IfCoLoG J. Log. Appl. 4(10), 3277\u20133356 (2017)","journal-title":"J. Appl. Log. - IfCoLoG J. Log. Appl."},{"issue":"7\u20138","key":"12_CR16","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1016\/j.apal.2013.01.002","volume":"164","author":"D Fern\u00e1ndez-Duque","year":"2013","unstructured":"Fern\u00e1ndez-Duque, D., Joosten, J.J.: Hyperations, Veblen progressions and transfinite iteration of ordinal functions. Ann. Pure Appl. Log. 164(7\u20138), 785\u2013801 (2013)","journal-title":"Ann. Pure Appl. Log."},{"key":"12_CR17","unstructured":"Fern\u00e1ndez-Duque, D., Joosten, J.J.: The omega-rule interpretation of transfinite provability logic. \nArXiv:1205.2036\n\n [math.LO] (2013)"},{"key":"12_CR18","unstructured":"Fern\u00e1ndez-Duque, D., Joosten, J.J.: Well-orders in the transfinite Japaridze algebra. \nArXiv:1212.3468\n\n [math.LO] (2013)"},{"key":"12_CR19","first-page":"327","volume-title":"Advances in Modal Logic","author":"E Hermo-Reyes","year":"2018","unstructured":"Hermo-Reyes, E., Joosten, J.J.: Relational semantics for the Turing Schmerl calculus. In: Bezhanishvili, G., D\u2019Agostino, G., Metcalfe, G., Studer, T. (eds.) Advances in Modal Logic, vol. 12, pp. 327\u2013346. College Publications, London (2018)"},{"key":"12_CR20","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1093\/logcom\/exp043","volume":"21","author":"TF Icard III","year":"2011","unstructured":"Icard III, T.F.: A topological study of the closed fragment of GLP. J. Log. Comput. 21, 683\u2013696 (2011)","journal-title":"J. Log. Comput."},{"key":"12_CR21","doi-asserted-by":"publisher","first-page":"249","DOI":"10.2307\/2275337","volume":"58","author":"KN Ignatiev","year":"1993","unstructured":"Ignatiev, K.N.: On strong provability predicates and the associated modal logics. J. Symb. Log. 58, 249\u2013290 (1993)","journal-title":"J. Symb. Log."},{"key":"12_CR22","unstructured":"Japaridze, G.K.: The modal logical means of investigation of provability. Ph.D. thesis, Moscow State University (1986). (in Russian)"},{"key":"12_CR23","series-title":"Monographs in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-44761-X","volume-title":"Set Theory, The Third Millenium Edition, Revised and Expanded","author":"T Jech","year":"2002","unstructured":"Jech, T.: Set Theory, The Third Millenium Edition, Revised and Expanded. Monographs in Mathematics. Springer, Heidelberg (2002). \nhttps:\/\/doi.org\/10.1007\/3-540-44761-X"},{"key":"12_CR24","unstructured":"Kreisel, G.: Wie die beweistheorie zu ihren ordinalzahlen kam und kommt. Jahresbericht der Deutschen Mathematiker-Vereinigung 78, 177\u2013224 (1976\/1977)"}],"container-title":["Lecture Notes in Computer Science","Logic, Language, Information, and Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-59533-6_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,6]],"date-time":"2019-12-06T15:02:59Z","timestamp":1575644579000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-59533-6_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783662595329","9783662595336"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-59533-6_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"9 June 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"WoLLIC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Logic, Language, Information, and Computation","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Utrecht","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"The Netherlands","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 July 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 July 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"wollic2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/wollic2019.sites.uu.nl\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"60","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"41","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"6","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"68% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2,3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"8","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}