{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T18:16:03Z","timestamp":1759342563035},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2004,9,1]],"date-time":"2004-09-01T00:00:00Z","timestamp":1093996800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2005,4]]},"DOI":"10.1007\/s00153-004-0232-4","type":"journal-article","created":{"date-parts":[[2004,8,31]],"date-time":"2004-08-31T05:17:57Z","timestamp":1093929477000},"page":"263-362","source":"Crossref","is-referenced-by-count":29,"title":["An ordinal analysis of parameter free ?12-comprehension"],"prefix":"10.1007","volume":"44","author":[{"given":"Michael","family":"Rathjen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2004,9,1]]},"reference":[{"key":"CR1","doi-asserted-by":"crossref","unstructured":"Barwise, J.: Admissible Sets and Structures. Springer, Berlin, 1975","DOI":"10.1007\/978-3-662-11035-5"},{"key":"CR2","doi-asserted-by":"crossref","unstructured":"Buchholz, W.: A simplified version of local predicativity. In: Aczel, Simmons, Wainer, (eds.), Leeds Proof Theory 1991, Cambridge University Press, Cambridge, 1993, pp. 115?147","DOI":"10.1017\/CBO9780511896262.006"},{"key":"CR3","doi-asserted-by":"crossref","unstructured":"Devlin, K.J.: Constructibility. Springer, Berlin, 1984","DOI":"10.1007\/978-3-662-21723-8"},{"key":"CR4","unstructured":"Drake, F.: Set Theory: An introduction to large cardinals. Amsterdam: North Holland, 1974"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2269764","volume":"29","author":"Feferman","year":"1964","unstructured":"Feferman, S.: Systems of predicative analysis. J. Symbolic Logic 29, 1?30 (1964)","journal-title":"J. Symbolic Logic"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"193","DOI":"10.2307\/2269866","volume":"23","author":"Feferman","year":"1968","unstructured":"Feferman, S.: Systems of predicative analysis II: representations of ordinals. J. Symbolic Logic 23, 193?220 (1968)","journal-title":"J. Symbolic Logic"},{"key":"CR7","unstructured":"Feferman, S.: Proof theory: a personal report. In: G. Takeuti, (ed.), Proof Theory, 2nd edition, North-Holland, Amsterdam, 1987, pp. 445?485"},{"key":"CR8","doi-asserted-by":"crossref","unstructured":"Feferman, S.: Remarks for ?The Trends in Logic?. In: Logic Colloquium ?88, North-Holland, Amsterdam, 1989, pp. 361?363","DOI":"10.1016\/S0049-237X(08)70276-3"},{"key":"CR9","unstructured":"Gentzen, G.: Stenogramm von G. Gentzen, 1945 Transcription by H. Kneser and H. Urban, 13 pages"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0003-4843(72)90001-0","volume":"4","author":"Jensen","year":"1972","unstructured":"Jensen, R.B.: The fine structure of the constructible hierarchy. Ann. Math. Logic 4, 229?308 (1972)","journal-title":"Ann. Math. Logic"},{"key":"CR11","unstructured":"Kanamori, A.: The higher infinite. Springer, Berlin, 1995"},{"key":"CR12","doi-asserted-by":"crossref","unstructured":"Kanamori, A., Magidor, M.: The evolution of large cardinal axioms in set theory. In: G. H. M\u00fcller, D.S. Scott (eds.) Higher Set Theory. Lecture Notes in Mathematics 669, Springer, Berlin, 1978, pp. 99?275","DOI":"10.1007\/BFb0103104"},{"key":"CR13","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/BF01621474","volume":"30","author":"Pohlers","year":"1991","unstructured":"Pohlers, W.: Proof theory and ordinal analysis. Arch. Math. Logic 30, 311?376 (1991)","journal-title":"Arch. Math. Logic"},{"key":"CR14","first-page":"47","volume":"39","author":"Rathjen","year":"1993","unstructured":"Rathjen, M.: How to develop proof?theoretic ordinal functions on the basis of admissible sets. Math. Quart. 39, 47?54 (1993)","journal-title":"Math. Quart."},{"key":"CR15","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BF01275469","volume":"33","author":"Rathjen","year":"1994","unstructured":"Rathjen, M.: Collapsing functions based on recursively large ordinals: A well?ordering proof for KPM. Arch. Math. Logic 33, 35?55 (1994)","journal-title":"Arch. Math. Logic"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0168-0072(94)90074-4","volume":"68","author":"Rathjen","year":"1994","unstructured":"Rathjen, M.: Proof theory of reflection. Ann. Pure Appl. Logic 68, 181?224 (1994)","journal-title":"Ann. Pure Appl. Logic"},{"key":"CR17","doi-asserted-by":"crossref","first-page":"468","DOI":"10.2307\/421132","volume":"1","author":"Rathjen","year":"1995","unstructured":"Rathjen, M.: Recent advances in ordinal analysis: ?12-CA and related systems. Bulletin of Symbolic Logic 1, 468?485 (1995)","journal-title":"Bulletin of Symbolic Logic"},{"key":"CR18","unstructured":"Rathjen, M.: An ordinal analysis of iterated ?12 comprehension and related systems. Preprint"},{"key":"CR19","doi-asserted-by":"crossref","first-page":"517","DOI":"10.2307\/2586483","volume":"64","author":"Rathjen","year":"1999","unstructured":"Rathjen, M.: Explicit mathematics with the monotone fixed point principle II. Models. J. Symbolic Logic 64, 517?550 (1999)","journal-title":"Models. J. Symbolic Logic"},{"key":"CR20","unstructured":"Rathjen, M.: An ordinal analysis of stability. To appear in: Archive for Mathematical Logic"},{"key":"CR21","unstructured":"Richter, W., Aczel, P.: Inductive definitions and reflecting properties of admissible ordinals. In: J.E. Fenstad, Hinman. (eds.), Generalized Recursion Theory, North Holland, Amsterdam, 1973, pp. 301?381"},{"key":"CR22","doi-asserted-by":"crossref","unstructured":"Sacks, G.E.: Higher recursion theory. Springer, Berlin, 1990","DOI":"10.1007\/978-3-662-12013-2"},{"key":"CR23","unstructured":"Schl\u00fcter, A.: Provability in set theories with reflection. Submitted"},{"key":"CR24","doi-asserted-by":"crossref","unstructured":"Sch\u00fctte, K.: Proof Theory. Springer, Berlin, 1977","DOI":"10.1007\/978-3-642-66473-1"},{"key":"CR25","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0003-4843(78)90031-1","volume":"13","author":"Solovay","year":"1978","unstructured":"Solovay, R.M., Reinhard, W.N., Kanamori, A.: Strong Axioms of Infinity and Elementary Embeddings, Ann. Math. Logic 13, 73?116 (1978)","journal-title":"Math. Logic"},{"key":"CR26","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/BF00486049","volume":"62","author":"Takeuti","year":"1985","unstructured":"Takeuti, G.: Proof theory and set theory. Synthese 62, 255?263 (1985)","journal-title":"Synthese"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/s00153-004-0232-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/article\/10.1007\/s00153-004-0232-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/s00153-004-0232-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,3]],"date-time":"2020-04-03T02:19:31Z","timestamp":1585880371000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/10.1007\/s00153-004-0232-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,9,1]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2005,4]]}},"alternative-id":["232"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s00153-004-0232-4","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,9,1]]}}}