{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T18:54:11Z","timestamp":1675882451743},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,12,10]],"date-time":"2009-12-10T00:00:00Z","timestamp":1260403200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2010,3]]},"DOI":"10.1007\/s00153-009-0168-9","type":"journal-article","created":{"date-parts":[[2009,12,9]],"date-time":"2009-12-09T14:34:23Z","timestamp":1260369263000},"page":"275-281","source":"Crossref","is-referenced-by-count":7,"title":["A note on the theory of positive induction, $${{\\rm ID}^*_1}$$"],"prefix":"10.1007","volume":"49","author":[{"given":"Bahareh","family":"Afshari","sequence":"first","affiliation":[]},{"given":"Michael","family":"Rathjen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,12,10]]},"reference":[{"key":"168_CR1","unstructured":"Aczel, P.: The Strength of Martin-L\u00f6f\u2019s Type Theory with One Universe. Technical report, Department of Philosophy, University of Helsinki (1977)"},{"key":"168_CR2","volume-title":"Relative Computability and the Proof-Theoretic Strengths of Some Theories. PhD thesis","author":"B. Afshari","year":"2008","unstructured":"Afshari B.: Relative Computability and the Proof-Theoretic Strengths of Some Theories. PhD thesis. University of Leeds, UK (2008)"},{"key":"168_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0091894","volume-title":"Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies Theories","author":"W. Buchholz","year":"1981","unstructured":"Buchholz W., Feferman S., Pohlers W., Sieg W.: Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies Theories. Springer-Verlag, Berlin, Heidelberg (1981)"},{"key":"168_CR4","unstructured":"Cantini, A.: A Note on a Predicatively Reducible Theory of Elementary Iterated Induction. Bollettino U.M.I 413\u2013430 (1985)"},{"key":"168_CR5","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1017\/S0022481200031224","volume":"51","author":"A. Cantini","year":"1986","unstructured":"Cantini A.: On the relation between choice and comprehension principles in second order arithmetic. J. Symb. Log. 51, 360\u2013373 (1986)","journal-title":"J. Symb. Log."},{"key":"168_CR6","first-page":"171","volume-title":"Iterated Inductive Fixed-Point Theories: Application to Hancock\u2019s Conjecture, Patras Logic Symposion","author":"S. Feferman","year":"1982","unstructured":"Feferman S.: Iterated Inductive Fixed-Point Theories: Application to Hancock\u2019s Conjecture, Patras Logic Symposion, pp. 171\u2013196. North-Holland, Amsterdam (1982)"},{"key":"168_CR7","unstructured":"Friedman, H.: Subtheories of Set Theory and Analysis, Dissertation, MIT (1967)"},{"key":"168_CR8","unstructured":"Friedman, H.: Theories of Inductive Definitions, Unpublished notes (1969)"},{"key":"168_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0168-0072(87)90073-X","volume":"33","author":"H. Friedman","year":"1987","unstructured":"Friedman H., Sheard M.: An axiomatic approach to self-referential truth. Ann. Pure Appl. Log. 33, 1\u201321 (1987)","journal-title":"Ann. Pure Appl. Log."},{"key":"168_CR10","doi-asserted-by":"crossref","first-page":"818","DOI":"10.2307\/2275787","volume":"61","author":"G. J\u00e4ger","year":"1996","unstructured":"J\u00e4ger G., Strahm T.: Some theories with positive induction of ordinal strength $${\\varphi\\omega 0}$$ . J. Symb. Log. 61, 818\u2013842 (1996)","journal-title":"J. Symb. Log."},{"key":"168_CR11","unstructured":"Kreisel, G.: Generalized Inductive Definitions. Technical report, Stanford University (1963)"},{"key":"168_CR12","doi-asserted-by":"crossref","unstructured":"Leigh, G., Rathjen, M.: An ordinal analysis for theories of self-referential truth. To appear in Arch. Math. Logic. doi: 10.1007\/s00153-009-0170-2","DOI":"10.1007\/s00153-009-0170-2"},{"key":"168_CR13","doi-asserted-by":"crossref","first-page":"721","DOI":"10.2178\/jsl\/1154698573","volume":"71","author":"D. Probst","year":"2006","unstructured":"Probst D.: The proof-theoretic analysis of transfinitely iterated quasi least fixed points. J. Symb. Log. 71, 721\u2013746 (2006)","journal-title":"J. Symb. Log."},{"key":"168_CR14","first-page":"239","volume-title":"Logic Colloquium \u201980","author":"S.G. Simpson","year":"1980","unstructured":"Simpson S.G.: $${\\Sigma^{1}_{1}}$$ and $${\\Pi^{1}_{1}}$$ transfinite induction. In: Dalen, D., Lascar, D., Smiley, TJ (eds) Logic Colloquium \u201980, pp. 239\u2013253. North-Holland, Amsterdam (1980)"},{"key":"168_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-59971-2","volume-title":"Subsystems of Second Order Arithmetic","author":"S.G. Simpson","year":"1999","unstructured":"Simpson S.G.: Subsystems of Second Order Arithmetic. Springer-Verlag, Berlin, Heidelberg (1999)"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-009-0168-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-009-0168-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-009-0168-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T19:36:43Z","timestamp":1558640203000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-009-0168-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12,10]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["168"],"URL":"https:\/\/doi.org\/10.1007\/s00153-009-0168-9","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12,10]]}}}