{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T08:37:53Z","timestamp":1743151073134,"version":"3.40.3"},"publisher-location":"Cham","reference-count":17,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030367541"},{"type":"electronic","value":"9783030367558"}],"license":[{"start":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T00:00:00Z","timestamp":1576800000000},"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":[[2020]]},"DOI":"10.1007\/978-3-030-36755-8_7","type":"book-chapter","created":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T10:05:16Z","timestamp":1576490716000},"page":"98-110","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finitism, Imperative Programs and Primitive Recursion"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4041-4382","authenticated-orcid":false,"given":"Daniel","family":"Leivant","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,12,20]]},"reference":[{"issue":"3","key":"7_CR1","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/S0168-0072(02)00030-1","volume":"118","author":"J Avigad","year":"2002","unstructured":"Avigad, J.: Saturated models of universal theories. Ann. Pure Appl. Log. 118(3), 219\u2013234 (2002)","journal-title":"Ann. Pure Appl. Log."},{"key":"7_CR2","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/S0049-237X(98)80017-7","volume-title":"Handbook of Proof Theory","author":"S Buss","year":"1998","unstructured":"Buss, S.: First-order proof theory of arithmetic. In: Buss, S.R. (ed.) Handbook of Proof Theory, pp. 79\u2013148. Elsevier, Amsterdam (1998)"},{"key":"7_CR3","unstructured":"Euclid: Elements. Dover, New York (1956)"},{"issue":"1","key":"7_CR4","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1305\/ndjfl\/1107220675","volume":"46","author":"F Ferreira","year":"2005","unstructured":"Ferreira, F.: A simple proof of Parsons\u2019 theorem. Notre Dame J. Formal Log. 46(1), 83\u201391 (2005)","journal-title":"Notre Dame J. Formal Log."},{"key":"7_CR5","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/BF01206605","volume":"95","author":"D Hilbert","year":"1926","unstructured":"Hilbert, D.: \u00dcber das unendliche. Math. Ann. 95, 161\u2013190 (1926)","journal-title":"Math. Ann."},{"key":"7_CR6","series-title":"Graduate Texts in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0539-5","volume-title":"Descriptive Complexity","author":"N Immerman","year":"1998","unstructured":"Immerman, N.: Descriptive Complexity. Graduate Texts in Computer Science. Springer, New York (1998). \nhttps:\/\/doi.org\/10.1007\/978-1-4612-0539-5"},{"key":"7_CR7","unstructured":"Leivant, D.: A theory of finite structures. Logical methods in computer science (2019, to appear). Preliminary version: \narXiv.org:1808.04949\n\n (2018)"},{"key":"7_CR8","unstructured":"Leivant, D., Marion, J.: Primitive recursion in the abstract. Mathematical structures in computer science (2019, to appear). Preliminary version under the title Implicit complexity via structure transformation, in \narXiv:1802.03115\n\n (2018)"},{"key":"7_CR9","series-title":"Encyclopedia of Mathematics","volume-title":"The Foundations of Mathematics in the Theory of Sets","author":"J Mayberry","year":"2000","unstructured":"Mayberry, J.: The Foundations of Mathematics in the Theory of Sets. Encyclopedia of Mathematics, vol. 82. Cambridge University Press, Cambridge (2000)"},{"key":"7_CR10","doi-asserted-by":"crossref","unstructured":"Meyer, A., Ritchie, D.: The complexity of loop programs. In: Proceedings of the 1967 22nd National Conference, New York, pp. 465\u2013469 (1967)","DOI":"10.1145\/800196.806014"},{"key":"7_CR11","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/BF01117472","volume":"1","author":"G Mints","year":"1972","unstructured":"Mints, G.: Quantifier-free and one-quantifier systems. J. Soviet Math. 1, 71\u201384 (1972)","journal-title":"J. Soviet Math."},{"key":"7_CR12","doi-asserted-by":"crossref","unstructured":"Parsons, C.: On a number theoretic choice schema and its relation to induction. In: Intuitionism and Proof Theory, North-Holland, Amsterdam , pp. 459\u2013473 (1970)","DOI":"10.1016\/S0049-237X(08)70771-7"},{"issue":"3","key":"7_CR13","doi-asserted-by":"publisher","first-page":"466","DOI":"10.2307\/2272731","volume":"37","author":"C Parsons","year":"1972","unstructured":"Parsons, C.: On n-quantier induction. J. Symb. Log. 37(3), 466\u2013482 (1972)","journal-title":"J. Symb. Log."},{"key":"7_CR14","unstructured":"Skolem, T.: Einige bemerkungen zur axiomatischen begr\u00fcndung der mengenlehre. In: Matematikerkongressen in Helsingfors Den femte skandinaviske matematikerkongressen (1922)"},{"key":"7_CR15","doi-asserted-by":"publisher","first-page":"524","DOI":"10.2307\/2026089","volume":"78","author":"W Tait","year":"1981","unstructured":"Tait, W.: Finitism. J. Philos. 78, 524\u2013546 (1981)","journal-title":"J. Philos."},{"key":"7_CR16","first-page":"53","volume":"17","author":"M Takahashi","year":"1969","unstructured":"Takahashi, M.: An induction principle in set theory I. Yokohama Math. J. 17, 53\u201359 (1969)","journal-title":"Yokohama Math. J."},{"key":"7_CR17","unstructured":"Takeuti, G.: Proof Theory. Amsterdam (1975)"}],"container-title":["Lecture Notes in Computer Science","Logical Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-36755-8_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T19:03:27Z","timestamp":1576782207000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-36755-8_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,20]]},"ISBN":["9783030367541","9783030367558"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-36755-8_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019,12,20]]},"assertion":[{"value":"20 December 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"LFCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Logical Foundations of Computer Science","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Deerfield Beach, FL","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 January 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 January 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"lfcs2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/lfcs.ws.gc.cuny.edu\/lfcs-2020\/","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":"30","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":"17","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":"0","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":"57% - 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":"3.3","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":"3.7","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":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}