{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T14:50:41Z","timestamp":1772376641756,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2017,2,20]],"date-time":"2017-02-20T00:00:00Z","timestamp":1487548800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001742","name":"United States-Israel Binational Science Foundation","doi-asserted-by":"publisher","award":["2010405"],"award-info":[{"award-number":["2010405"]}],"id":[{"id":"10.13039\/501100001742","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2017,5]]},"DOI":"10.1007\/s00153-017-0524-0","type":"journal-article","created":{"date-parts":[[2017,2,20]],"date-time":"2017-02-20T04:27:12Z","timestamp":1487564832000},"page":"319-383","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A parallel to the null ideal for inaccessible $$\\lambda $$ \u03bb : Part I"],"prefix":"10.1007","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0462-3152","authenticated-orcid":false,"given":"Saharon","family":"Shelah","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,2,20]]},"reference":[{"key":"524_CR1","doi-asserted-by":"crossref","DOI":"10.1201\/9781439863466","volume-title":"Set Theory: On the Structure of the Real Line","author":"T Bartoszy\u0144ski","year":"1995","unstructured":"Bartoszy\u0144ski, T., Judah, H.: Set Theory: On the Structure of the Real Line. A K Peters, Wellesley (1995)"},{"key":"524_CR2","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/978-1-4020-5764-9_7","volume-title":"Handbook of Set Theory","author":"A Blass","year":"2010","unstructured":"Blass, A.: Combinatorial cardinal characteristics of the continuum. In: Foreman, M., Kanamori, A. (eds.) Handbook of Set Theory, pp. 395\u2013490. Springer, New York (2010)"},{"key":"524_CR3","unstructured":"Brendle, J., Shelah, S.: Ultrafilters on $$\\omega $$ \u03c9 -their ideals and their cardinal characteristics. Trans. Am. Math. Soc. 351, 2643\u20132674 (1999). arXiv:math.LO\/9710217"},{"key":"524_CR4","unstructured":"Cohen, S., Shelah, S.: On a parallel of random real forcing for inaccessible cardinals (2016) arXiv:1603.08362 [math.LO]"},{"key":"524_CR5","unstructured":"Cummings, J., Shelah, S.: Cardinal invariants above the continuum. Ann. Pure Appl. Log. 75, 251\u2013268 (1995). arXiv:math.LO\/9509228"},{"key":"524_CR6","unstructured":"Fremlin, D.H.: Measure Theory, vol. 1\u20135. Torres Fremlin, Colchester (2004). https:\/\/www.essex.ac.uk\/maths\/people\/fremlin\/mt.htm"},{"key":"524_CR7","unstructured":"Grossberg, R., Shelah, S.: On cardinalities in quotients of inverse limits of groups. Math. Jpn. 47, 189\u2013197 (1998). arXiv:math\/9911225 [math.LO]"},{"key":"524_CR8","unstructured":"Halko, A., Shelah, S.: On strong measure zero subsets of $${}^\\kappa 2$$ \u03ba 2 . Fundam. Math. 170, 219\u2013229 (2001). arXiv:math.LO\/9710218"},{"key":"524_CR9","doi-asserted-by":"crossref","first-page":"33","DOI":"10.2307\/2273317","volume":"48","author":"M Magidor","year":"1983","unstructured":"Magidor, M., Shelah, S., Stavi, J.: On the standard part of nonstandard models of set theory. J. Symb. Log. 48, 33\u201338 (1983)","journal-title":"J. Symb. Log."},{"key":"524_CR10","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0168-0072(84)90006-X","volume":"26","author":"M Magidor","year":"1984","unstructured":"Magidor, M., Shelah, S., Stavi, J.: Countably decomposable admissible sets. Ann. Pure Appl. Log. 26, 287\u2013361 (1984). Proceedings of the 1980\/1 Jerusalem Model Theory year","journal-title":"Ann. Pure Appl. Log."},{"key":"524_CR11","doi-asserted-by":"crossref","first-page":"8139","DOI":"10.1090\/S0002-9947-2015-06303-X","volume":"367","author":"M Malliaris","year":"2015","unstructured":"Malliaris, M., Shelah, S.: Constructing regular ultrafilters from a model-theoretic point of view. Trans. Am. Math. Soc. 367, 8139\u20138173 (2015)","journal-title":"Trans. Am. Math. Soc."},{"key":"524_CR12","doi-asserted-by":"crossref","unstructured":"Malliaris, M., Shelah, S.: Cofinality spectrum theorems in model theory, set theory and general topology. J. Am. Math. Soc. 29, 237\u2013297 (2016). arXiv:1208.5424","DOI":"10.1090\/jams830"},{"key":"524_CR13","unstructured":"Matet, P., Ros\u0142anowski, A., Shelah, S.: Cofinality of the nonstationary ideal. Trans. Am. Math. Soc. 357, 4813\u20134837 (2005). arXiv:math.LO\/0210087"},{"key":"524_CR14","doi-asserted-by":"crossref","unstructured":"Oxtoby, J.C.: Measure and Category. A Survey of the Analogies Between Topological and Measure Spaces. Graduate Texts in Mathematics, vol. 2. Springer, New York (1980)","DOI":"10.1007\/978-1-4684-9339-9"},{"key":"524_CR15","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1515\/JAA.1997.103","volume":"3","author":"A Ros\u0142anowski","year":"1997","unstructured":"Ros\u0142anowski, A., Shelah, S.: Norms on possibilities II: More ccc ideals on $$2^{\\textstyle \\omega }$$ 2 \u03c9 . J. Appl. Anal. 3, 103\u2013127 (1997). arxiv:math.LO\/9703222","journal-title":"J. Appl. Anal."},{"key":"524_CR16","unstructured":"Ros\u0142anowski, A., Shelah, S.: Sweet & sour and other flavours of ccc forcing notions. Arch. Math. Log. 43, 583\u2013663 (2004). arXiv:math.LO\/9909115"},{"key":"524_CR17","unstructured":"Ros\u0142anowski, A., Shelah, S.: How much sweetness is there in the universe? Math. Log. Q. 52, 71\u201386 (2006). arXiv:math.LO\/0406612"},{"key":"524_CR18","unstructured":"Ros\u0142anowski, A., Shelah, S.: Reasonably complete forcing notions. Quad. Mat. 17, 195\u2013239 (2006). arXiv:math.LO\/0508272"},{"key":"524_CR19","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s11856-007-0040-8","volume":"159","author":"A Ros\u0142anowski","year":"2007","unstructured":"Ros\u0142anowski, A., Shelah, S.: Sheva\u2013Sheva\u2013Sheva: large creatures. Isr. J. Math. 159, 109\u2013174 (2007). arxiv:math.LO\/0210205","journal-title":"Isr. J. Math."},{"key":"524_CR20","unstructured":"Ros\u0142anowski, A., Shelah, S.: Generating ultrafilters in a reasonable way. Math. Log. Q. 54, 202\u2013220 (2008). arXiv:math.LO\/0607218"},{"key":"524_CR21","unstructured":"Ros\u0142anowski, A., Shelah, S.: Lords of the iteration. In: Set Theory and Its Applications, volume 533 of Contemporary Mathematics (CONM), pp. 287\u2013330. American Mathematical Society (2011). arxiv:math.LO\/0611131"},{"key":"524_CR22","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1215\/00294527-1306154","volume":"52","author":"A Ros\u0142anowski","year":"2011","unstructured":"Ros\u0142anowski, A., Shelah, S.: Reasonable ultrafilters, again. Notre Dame J. Form. Log. 52, 113\u2013147 (2011). arxiv:math.LO\/0605067","journal-title":"Notre Dame J. Form. Log."},{"key":"524_CR23","doi-asserted-by":"crossref","unstructured":"Ros\u0142anowski, A., Shelah, S.: More about $$\\lambda $$ \u03bb -support iterations of $$({<}\\lambda )$$ ( < \u03bb ) -complete forcing notions. Arch. Math. Log. 52, 603\u2013629 (2013). arXiv:1105.6049","DOI":"10.1007\/s00153-013-0334-y"},{"key":"524_CR24","unstructured":"Shelah, S.: Bounding forcing with chain conditions for uncountable cardinals. http:\/\/shelah.logic.at\/E82_abs.html . Accessed 15 Feb 2017"},{"key":"524_CR25","unstructured":"Shelah, S.: Creature iteration for inaccesibles. http:\/\/shelah.logic.at\/1100_abs.html . Accessed 15 Feb 2017"},{"key":"524_CR26","unstructured":"Shelah, S.: Iterations adding no $$\\lambda $$ \u03bb -Cohen (in preparation)"},{"key":"524_CR27","unstructured":"Shelah, S.: On CON( $$\\mathfrak{d}_\\lambda >\\text{cov}_\\lambda $$ d \u03bb > cov \u03bb (meagre)). Trans. Am. Math. Soc. arxiv:0904.0817"},{"key":"524_CR28","unstructured":"Shelah, S.: Random $$\\lambda $$ \u03bb -reals for inaccessible continued (in preparation)"},{"key":"524_CR29","unstructured":"Shelah, S.: The null ideal for uncountable cardinals (in preparation)"},{"key":"524_CR30","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1090\/S0002-9939-1988-0943095-3","volume":"103","author":"S Shelah","year":"1988","unstructured":"Shelah, S.: Can the fundamental (homotopy) group of a space be the rationals? Proc. Am. Math. Soc. 103, 627\u2013632 (1988)","journal-title":"Proc. Am. Math. Soc."},{"key":"524_CR31","unstructured":"Shelah, S.: Classification theory and the number of nonisomorphic models. In: Barwise, J., Keisler, H.J., Suppes, P., Troelstra, A.S. (eds.) Studies in Logic and the Foundations of Mathematics, vol. 92. North-Holland, Amsterdam (1990)"},{"key":"524_CR32","unstructured":"Shelah, S.: Vive la diff\u00e9rence I: nonisomorphism of ultrapowers of countable models. In: Set Theory of the Continuum, volume\u00a026 of Mathematical Sciences Research Institute Publications, pp. 357\u2013405. Springer, Berlin (1992). arxiv:math.LO\/9201245"},{"key":"524_CR33","doi-asserted-by":"crossref","unstructured":"Shelah, S.: How special are Cohen and random forcings i.e. Boolean algebras of the family of subsets of reals modulo meagre or null. Isr. J. Math. 88, 159\u2013174 (1994). arXiv:math.LO\/9303208","DOI":"10.1007\/BF02937509"},{"key":"524_CR34","doi-asserted-by":"crossref","unstructured":"Shelah, S.: Proper and improper forcing. In: Feferman, S., Hodges, W.A., Lerman, M., Macintyre, A.J., Magidor, M., Moschovakis, Y.M. (eds.) Perspectives in Mathematical Logic. Springer, Berlin (1998)","DOI":"10.1007\/978-3-662-12831-2"},{"key":"524_CR35","doi-asserted-by":"crossref","unstructured":"Shelah, S.: Consistently there is no non trivial ccc forcing notion with the Sacks or Laver property. Combinatorica 21, 309\u2013319 (2001). arXiv:math.LO\/0003139","DOI":"10.1007\/s004930100027"},{"key":"524_CR36","doi-asserted-by":"crossref","unstructured":"Shelah, S.: Strong dichotomy of cardinality. Results Math. 39, 131\u2013154 (2001). arXiv:math.LO\/9807183","DOI":"10.1007\/BF03322680"},{"key":"524_CR37","unstructured":"Shelah, S.: On nice equivalence relations on $${}^\\lambda 2$$ \u03bb 2 . Arch. Math. Log. 43, 31\u201364 (2004). arXiv:math.LO\/0009064"},{"key":"524_CR38","unstructured":"Shelah, S.: Properness without elementaricity. J. Appl. Anal. 10, 168\u2013289 (2004). arXiv:math.LO\/9712283"},{"key":"524_CR39","unstructured":"Shelah, S.: Quite complete real closed fields. Isr. J. Math. 142, 261\u2013272 (2004). arXiv:math.LO\/0112212"},{"key":"524_CR40","unstructured":"Shelah, S.: On nicely definable forcing notions. J. Appl. Anal. 111(1), 1\u201317 (2005). arXiv:math.LO\/0303293"},{"key":"524_CR41","unstructured":"Shelah, S.: The combinatorics of reasonable ultrafilters. Fundam. Math. 192, 1\u201323 (2006). arXiv:math.LO\/0407498"},{"key":"524_CR42","unstructured":"Shelah, S.: The spectrum of characters of ultrafilters on $$\\omega $$ \u03c9 . Colloq. Math. 111(2), 213\u2013220 (2008). arXiv:math.LO\/0612240"},{"key":"524_CR43","unstructured":"Shelah, S.: Polish algebras, shy from freedom. Isr. J. Math. 181, 477\u2013507 (2011). arXiv:math.LO\/0212250"},{"key":"524_CR44","unstructured":"Shelah, S.: The character spectrum of $$\\beta (N)$$ \u03b2 ( N ) . Topol. Appl. 158, 2535\u20132555 (2011). arXiv:1004.2083"},{"key":"524_CR45","unstructured":"Shelah, S., V\u00e4is\u00e4nen, P.: On equivalence relations second order definable over $$H(\\kappa )$$ H ( \u03ba ) . Fundam. Math. 174, 1\u201321 (2002). arXiv:math.LO\/9911231"},{"key":"524_CR46","unstructured":"Shelah, S., V\u00e4is\u00e4nen, P.: The number of $$L_{\\infty \\kappa }$$ L \u221e \u03ba -equivalent nonisomorphic models for $$\\kappa $$ \u03ba weakly compact. Fundam. Math. 174, 97\u2013126 (2002). arXiv:math.LO\/9911232"},{"key":"524_CR47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1970696","volume":"92","author":"RM Solovay","year":"1970","unstructured":"Solovay, R.M.: A model of set theory in which every set of reals is Lebesgue measurable. Ann. Math. 92, 1\u201356 (1970)","journal-title":"Ann. Math."}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-017-0524-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-017-0524-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-017-0524-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T17:47:12Z","timestamp":1568828832000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-017-0524-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,20]]},"references-count":47,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2017,5]]}},"alternative-id":["524"],"URL":"https:\/\/doi.org\/10.1007\/s00153-017-0524-0","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,20]]}}}