{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T16:00:00Z","timestamp":1721923200676},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2011,12,9]],"date-time":"2011-12-09T00:00:00Z","timestamp":1323388800000},"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":[[2012,2]]},"DOI":"10.1007\/s00153-011-0258-3","type":"journal-article","created":{"date-parts":[[2011,12,8]],"date-time":"2011-12-08T13:17:18Z","timestamp":1323350238000},"page":"127-161","source":"Crossref","is-referenced-by-count":4,"title":["Phase transitions of iterated Higman-style well-partial-orderings"],"prefix":"10.1007","volume":"51","author":[{"given":"Lev","family":"Gordeev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Weiermann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,12,9]]},"reference":[{"issue":"1","key":"258_CR1","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1002\/1521-3870(200201)48:1<125::AID-MALQ125>3.0.CO;2-N","volume":"48","author":"T. Arai","year":"2002","unstructured":"Arai T.: On the slowly well orderedness of $${\\varepsilon _{0}}$$ . Math. Log. Q. 48(1), 125\u2013130 (2002)","journal-title":"Math. Log. Q."},{"key":"258_CR2","unstructured":"Bovykin, A., Weiermann, A.: Unprovability, Phase Transitions and the Riemann Zeta Function. New Directions in Value-Distribution Theory of Zeta and L-Functions. Shaker-Verlag 19\u201337 (2009)"},{"issue":"2","key":"258_CR3","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1002\/malq.19940400212","volume":"40","author":"W. Buchholz","year":"1994","unstructured":"Buchholz W., Cichon E.A., Weiermann A.: A uniform approach to fundamental sequences and hierarchies. Math. Log. Q. 40(2), 273\u2013286 (1994)","journal-title":"Math. Log. Q."},{"key":"258_CR4","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511801655","volume-title":"Analytic Combinatorics","author":"Ph. Flajolet","year":"2009","unstructured":"Flajolet Ph., Sedgewick R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009)"},{"key":"258_CR5","doi-asserted-by":"crossref","first-page":"100","DOI":"10.2307\/2275019","volume":"54","author":"L. Gordeev","year":"1987","unstructured":"Gordeev L.: Generalizations of the one-dimensional version of the Kruskal-Friedman theorems. J. Symb. Log. 54, 100\u2013121 (1987)","journal-title":"J. Symb. Log."},{"key":"258_CR6","doi-asserted-by":"crossref","first-page":"157","DOI":"10.2307\/2274960","volume":"55","author":"L. Gordeev","year":"1990","unstructured":"Gordeev L.: Generalizations of the Kruskal-Friedman theorems. J. Symb. Log. 55, 157\u2013181 (1990)","journal-title":"J. Symb. Log."},{"key":"258_CR7","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1090\/conm\/147\/01194","volume":"147","author":"L. Gordeev","year":"1993","unstructured":"Gordeev L.: Quasi-Ordinals and proof theory. Proc. Conf. Graph Minors. Contemp. Math. 147, 485\u2013494 (1993)","journal-title":"Proc. Conf. Graph Minors. Contemp. Math."},{"key":"258_CR8","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.2307\/2275697","volume":"59","author":"L. Gordeev","year":"1994","unstructured":"Gordeev L.: A modified sentence unprovable in PA. J. Symb. Log. 59, 1154\u20131157 (1994)","journal-title":"J. Symb. Log."},{"key":"258_CR9","doi-asserted-by":"crossref","unstructured":"Gordeev, L., Weiermann, A.: Phase Transitions in Proof Theory. DMTCS proc. AM, pp. 343\u2013358 (2010)","DOI":"10.46298\/dmtcs.2771"},{"issue":"1","key":"258_CR10","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s11083-007-9058-0","volume":"24","author":"A. Montalb\u00e1n","year":"2007","unstructured":"Montalb\u00e1n A.: Computable linearizations of well-partial-orderings. Order 24(1), 39\u201348 (2007)","journal-title":"Order"},{"key":"258_CR11","volume-title":"Handbook of Mathematical Logic","author":"J. Paris","year":"1977","unstructured":"Paris J., Harrington L.: A mathematical incompleteness in Peano arithmetic. In: Barwise, J. (eds) Handbook of Mathematical Logic, North-Holland, Amsterdam (1977)"},{"key":"258_CR12","doi-asserted-by":"crossref","unstructured":"Smith, R.: The consistency strength of some finite forms of the Higman and Kruskal theorems. In: Harvey Friedman\u2019s Research on the Foundations of Mathematics, pp. 119\u2013136. North-Holland, Amsterdam (1985)","DOI":"10.1016\/S0049-237X(09)70157-0"},{"key":"258_CR13","doi-asserted-by":"crossref","first-page":"5","DOI":"10.2178\/jsl\/1045861503","volume":"68","author":"A. Weiermann","year":"2003","unstructured":"Weiermann A.: An application of graphical enumeration to PA. J. Symb. Log. 68, 5\u201316 (2003)","journal-title":"J. Symb. Log."},{"key":"258_CR14","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1090\/S0002-9939-03-07086-2","volume":"132","author":"A. Weiermann","year":"2004","unstructured":"Weiermann A.: A classification of rapidly growing Ramsey functions. Proc. Am. Math. Soc. 132, 553\u2013561 (2004)","journal-title":"Proc. Am. Math. Soc."},{"issue":"2","key":"258_CR15","doi-asserted-by":"crossref","first-page":"177","DOI":"10.2178\/bsl\/1146620058","volume":"12","author":"A. Weiermann","year":"2006","unstructured":"Weiermann A.: Classifying the provably total functions of PA. Bull. Symb. Log. 12(2), 177\u2013190 (2006)","journal-title":"Bull. Symb. Log."},{"issue":"1","key":"258_CR16","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1002\/malq.200610022","volume":"53","author":"A. Weiermann","year":"2007","unstructured":"Weiermann A.: Phase transition thresholds for some Friedman-style independence results. Math. Log. Q. 53(1), 4\u201318 (2007)","journal-title":"Math. Log. Q."},{"issue":"2\u20133","key":"258_CR17","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.apal.2008.09.012","volume":"157","author":"A. Weiermann","year":"2009","unstructured":"Weiermann A.: Phase transitions for G\u00f6del incompleteness. Ann. Pure Appl. Log. 157(2\u20133), 281\u2013296 (2009)","journal-title":"Ann. Pure Appl. Log."}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-011-0258-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-011-0258-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-011-0258-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,19]],"date-time":"2021-12-19T10:52:47Z","timestamp":1639911167000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-011-0258-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,9]]},"references-count":17,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,2]]}},"alternative-id":["258"],"URL":"https:\/\/doi.org\/10.1007\/s00153-011-0258-3","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,12,9]]}}}