{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T05:48:36Z","timestamp":1719467316738},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2016,1,12]],"date-time":"2016-01-12T00:00:00Z","timestamp":1452556800000},"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":["Arch. Math. Logic"],"published-print":{"date-parts":[[2016,2]]},"DOI":"10.1007\/s00153-015-0469-0","type":"journal-article","created":{"date-parts":[[2016,1,12]],"date-time":"2016-01-12T13:37:17Z","timestamp":1452605837000},"page":"239-294","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["ZF\u00a0+\u00a0DC\u00a0+\u00a0AX4"],"prefix":"10.1007","volume":"55","author":[{"given":"Saharon","family":"Shelah","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,1,12]]},"reference":[{"key":"469_CR1","doi-asserted-by":"crossref","unstructured":"Eklof, P.C., Mekler, A.: Almost Free Modules: Set Theoretic Methods, North\u2013Holland Mathematical Library, vol. 65, Revised edn. North\u2013Holland Publishing Co., Amsterdam (2002)","DOI":"10.1016\/S0924-6509(02)80006-X"},{"key":"469_CR2","unstructured":"Dzamonja, M., Shelah, S.: On squares, outside guessing of clubs and $${I_{<f}[\\lambda]}$$ I < f [ \u03bb ] . Fundam. Math. 148, 165\u2013198 (1995). arXiv:math.LO\/9510216"},{"key":"469_CR3","first-page":"901","volume":"191","author":"M. Gitik","year":"2012","unstructured":"Gitik M., K\u00f6epke P.: Violating the singular cardinals hypothesis without large cardinals Isr. J. Math. 191, 901\u2013922 (2012)","journal-title":"J. Math."},{"key":"469_CR4","doi-asserted-by":"crossref","unstructured":"G\u00f6bel, R., Trlifaj, J.: Approximations and Endomorphism Algebras of Modules, vols. I, II. de Gruyter Expositions in Mathematics. Walter de Gruyter, Berlin\/Boston (2012)","DOI":"10.1515\/9783110218114"},{"key":"469_CR5","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s00025-009-0382-0","volume":"54","author":"R. G\u00f6bel","year":"2009","unstructured":"G\u00f6bel R., Shelah S.: $${\\aleph_n}$$ \u2135 n -free modules with trivial dual. Results Math. 54, 53\u201364 (2009)","journal-title":"Results Math."},{"key":"469_CR6","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.4171\/JEMS\/475","volume":"16","author":"R. G\u00f6bel","year":"2014","unstructured":"G\u00f6bel R., Herden D., Shelah S.: Prescribing endomorphism rings of $${\\aleph_n}$$ \u2135 n -free modules. J. Eur. Math. Soc. 16, 1775\u20131816 (2014)","journal-title":"J. Eur. Math. Soc."},{"key":"469_CR7","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1017\/S0017089512000614","volume":"55","author":"R. G\u00f6bel","year":"2013","unstructured":"G\u00f6bel R., Shelah S., Struengmann L.: $${\\aleph_n}$$ \u2135 n -free modules over complete discrete valuation domains with small dual. Glasg. Math. J. 55, 369\u2013380 (2013)","journal-title":"Glasg. Math. J."},{"key":"469_CR8","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1002\/malq.200810011","volume":"55","author":"P. Larson","year":"2009","unstructured":"Larson P., Shelah S.: Splitting stationary sets from weak forms of choice. Math. Log. Q. 55, 299\u2013306 (2009)","journal-title":"Math. Log. Q."},{"key":"469_CR9","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0168-0072(87)90075-3","volume":"33","author":"M. Rubin","year":"1987","unstructured":"Rubin M., Shelah S.: Combinatorial problems on trees: partitions, \u0394-systems and large free subtrees. Ann. Pure Appl. Log. 33, 43\u201381 (1987)","journal-title":"Ann. Pure Appl. Log."},{"key":"469_CR10","doi-asserted-by":"crossref","unstructured":"Shelah, S.: Proper Forcing, Lecture Notes in Mathematics, vol. 940, Springer, Berlin, xxix+496\u00a0pp (1982)","DOI":"10.1007\/978-3-662-21543-2"},{"key":"469_CR11","doi-asserted-by":"crossref","unstructured":"Shelah, S.: Cardinal Arithmetic, Oxford Logic Guides, vol. 29. Oxford University Press, Oxford (1994)","DOI":"10.1093\/oso\/9780198537854.001.0001"},{"key":"469_CR12","unstructured":"Shelah, S.: Combinatorial Background for Non-structure arXiv:1512.04767 [math.LO]"},{"key":"469_CR13","unstructured":"Shelah, S.: PCF: The Advanced PCF Theorems. arXiv:1512.07063"},{"key":"469_CR14","doi-asserted-by":"crossref","unstructured":"Shelah, S.: A combinatorial principle and endomorphism rings. I. On p-groups. Isr. J. Math. 49, 239\u2013257 (1984). Proceedings of the 1980\/1 Jerusalem Model Theory year","DOI":"10.1007\/BF02760650"},{"key":"469_CR15","unstructured":"Shelah, S.: Black Boxes. arXiv:0812.0656"},{"key":"469_CR16","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/BF02807866","volume":"70","author":"S. Shelah","year":"1990","unstructured":"Shelah S.: Products of regular cardinals and cardinal invariants of products of Boolean algebras. Isr. J. Math. 70, 129\u2013187 (1990)","journal-title":"Isr. J. Math."},{"key":"469_CR17","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/BF01370693","volume":"31","author":"S. Shelah","year":"1991","unstructured":"Shelah S.: Reflecting stationary sets and successors of singular cardinals. Arch. Math. Log. 31, 25\u201353 (1991)","journal-title":"Arch. Math. Log."},{"key":"469_CR18","unstructured":"Shelah, Saharon: Further cardinal arithmetic. Isr. J. Math. 95, 61\u2013114 (1996). arXiv:math.LO\/9610226"},{"key":"469_CR19","unstructured":"Shelah, S.: The generalized continuum hypothesis revisited. Isr. J. Math. 116, 285\u2013321 (2000). arXiv:math.LO\/9809200"},{"key":"469_CR20","doi-asserted-by":"crossref","unstructured":"Shelah, S.: Set theory without choice: not everything on cofinality is possible. Arch. Math. Log. 36, 81\u2013125 (1997). A special volume dedicated to Prof. Azriel Levy. arXiv:math.LO\/9512227","DOI":"10.1007\/s001530050057"},{"key":"469_CR21","unstructured":"Shelah, S.: The pcf-theorem revisited. In: Graham, N. (eds) The Mathematics of Paul Erd\u0151s, II, Algorithms and Combinatorics, vol. 14, pp. 420\u2013459. Springer (1997). arXiv:math.LO\/9502233"},{"key":"469_CR22","doi-asserted-by":"crossref","unstructured":"Shelah, S.: More on the Revised GCH and the Black Box. Ann. Pure Appl. Log. 140, 133\u2013160 (2006). arXiv:math.LO\/0406482","DOI":"10.1016\/j.apal.2005.09.013"},{"key":"469_CR23","unstructured":"Shelah, S.: PCF without choice. Arch. Math. Log. submitted. arXiv:math.LO\/0510229"},{"key":"469_CR24","unstructured":"Shelah, S.: $${\\aleph_n}$$ \u2135 n -free abelain group with no non-zero homomorphism to $${\\mathbb{Z}}$$ Z . CUBO Math. J. 9, 59\u201379 (2007). arXiv:math.LO\/0609634"},{"key":"469_CR25","unstructured":"Shelah, S.: Models of expansions of $${\\mathbb{N}}$$ N with no end extensions. Math. Log. Q. 57, 341\u2013365 (2011). arXiv:0808.2960"},{"key":"469_CR26","unstructured":"Shelah, S.: PCF arithmetic without and with choice. Isr. J. Math. 191, 1\u201340 (2012). arXiv:0905.3021"},{"key":"469_CR27","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/s11856-014-1063-6","volume":"201","author":"S. Shelah","year":"2014","unstructured":"Shelah S.: Pseudo pcf. Isr. J. Math. 201, 185\u2013231 (2014)","journal-title":"Isr. J. Math."},{"key":"469_CR28","unstructured":"Shelah, S.: Quite free complicated abelian groups, PCF and Black Boxes, Isr. J. Math. submitted"},{"key":"469_CR29","unstructured":"Shelah, S.: Set theory with weak choice: Ax 4 and Abelian groups (in preparation)"},{"key":"469_CR30","doi-asserted-by":"crossref","unstructured":"Shelah, S. and Kojman, The PCF trichotomy theorem does not hold for short sequences, Arch. Math. Log. 39, 213\u2013218 (2000)","DOI":"10.1007\/s001530050143"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-015-0469-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-015-0469-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-015-0469-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T19:27:21Z","timestamp":1718306841000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-015-0469-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,12]]},"references-count":30,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2016,2]]}},"alternative-id":["469"],"URL":"https:\/\/doi.org\/10.1007\/s00153-015-0469-0","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,12]]}}}