{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:31:12Z","timestamp":1775838672644,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"5-6","license":[{"start":{"date-parts":[[2014,6,3]],"date-time":"2014-06-03T00:00:00Z","timestamp":1401753600000},"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":[[2014,8]]},"DOI":"10.1007\/s00153-014-0385-8","type":"journal-article","created":{"date-parts":[[2014,6,2]],"date-time":"2014-06-02T20:20:31Z","timestamp":1401740431000},"page":"695-729","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Cicho\u0144\u2019s diagram, regularity properties and $${\\varvec{\\Delta}^1_3}$$ \u0394 3 1 sets of reals"],"prefix":"10.1007","volume":"53","author":[{"given":"Vera","family":"Fischer","sequence":"first","affiliation":[]},{"given":"Sy David","family":"Friedman","sequence":"additional","affiliation":[]},{"given":"Yurii","family":"Khomskii","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,6,3]]},"reference":[{"key":"385_CR1","unstructured":"Bagaria, J., Friedman, S.D.: Generic absoluteness. In: Proceedings of the 11th Latin American Symposium on Mathematical Logic (M\u00e9rida, 1998), vol. 108, pp. 3\u201313 (2001)"},{"issue":"4","key":"385_CR2","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.2307\/2275649","volume":"62","author":"J. Bagaria","year":"1997","unstructured":"Bagaria J., Woodin W.H.: $${{\\varvec{\\Delta}}^1_n }$$ \u0394 n 1 sets of reals. J. Symb. Logic 62(4), 1379\u20131428 (1997)","journal-title":"J. Symb. Logic"},{"key":"385_CR3","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, USA (1995)"},{"key":"385_CR4","doi-asserted-by":"crossref","unstructured":"Brendle, J.: How small can the set of generics be? In: Logic Colloquium \u201998 (Prague), vol. 13 of Lecturer Notes Log., pp. 109\u2013126. Assoc. Symb. Logic, Urbana, IL (2000)","DOI":"10.1017\/9781316756140.010"},{"key":"385_CR5","unstructured":"Brendle, J.: Forcing and the structure of the real line: the Bogot\u00e1 lectures. Lecture notes (2009)"},{"issue":"1","key":"385_CR6","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1017\/S0305004104008187","volume":"138","author":"J. Brendle","year":"2005","unstructured":"Brendle J., Halbeisen L., L\u00f6we B.: Silver measurability and its relation to other regularity properties. Math. Proc. Camb. Philos. Soc. 138(1), 135\u2013149 (2005)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"issue":"9","key":"385_CR7","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1016\/j.apal.2012.03.003","volume":"163","author":"J. Brendle","year":"2012","unstructured":"Brendle J., Khomskii Y.: Polarized partitions on the second level of the projective hierarchy. Ann. Pure Appl. Logic 163(9), 1345\u20131357 (2012)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"3","key":"385_CR8","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.2307\/2586632","volume":"64","author":"J. Brendle","year":"1999","unstructured":"Brendle J., L\u00f6we B.: Solovay-type characterizations for forcing-algebras. J. Symb. Logic 64(3), 1307\u20131323 (1999)","journal-title":"J. Symb. Logic"},{"issue":"1","key":"385_CR9","doi-asserted-by":"crossref","first-page":"137","DOI":"10.2969\/jmsj\/06310137","volume":"63","author":"J. Brendle","year":"2011","unstructured":"Brendle J., L\u00f6we B.: Eventually different functions and inaccessible cardinals. J. Math. Soc.Jpn. 63(1), 137\u2013151 (2011)","journal-title":"J. Math. Soc.Jpn."},{"key":"385_CR10","doi-asserted-by":"crossref","unstructured":"David, R.: $${\\Delta^{1}_{3}}$$ \u0394 3 1 reals. Ann. Math. Logic 23(2\u20133), 121\u2013125 (1983), 1982","DOI":"10.1016\/0003-4843(82)90002-X"},{"issue":"1","key":"385_CR11","doi-asserted-by":"crossref","first-page":"461","DOI":"10.2307\/2586548","volume":"65","author":"C.A. Prisco Di","year":"2000","unstructured":"Di Prisco C.A., Henle J.M.: Doughnuts, floating ordinals, square brackets, and ultraflitters. J. Symb. Logic 65(1), 461\u2013473 (2000)","journal-title":"J. Symb. Logic"},{"issue":"1","key":"385_CR12","first-page":"241","volume":"108","author":"A. Dow","year":"1990","unstructured":"Dow A.: Two classes of Fr\u00e9chet\u2013Urysohn spaces. Proc. Am. Math. Soc. 108(1), 241\u2013247 (1990)","journal-title":"Proc. Am. Math. Soc."},{"key":"385_CR13","doi-asserted-by":"crossref","unstructured":"Feng, Q., Magidor, M., Woodin, H.: Universally Baire sets of reals. In: Set Theory of the Continuum (Berkeley, CA, 1989), vol. 26 of Math. Sci. Res. Inst. Publ., pp 203\u2013242. Springer, New York (1992)","DOI":"10.1007\/978-1-4613-9754-0_15"},{"issue":"7","key":"385_CR14","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1016\/j.apal.2009.11.003","volume":"161","author":"V. Fischer","year":"2010","unstructured":"Fischer V., Friedman S.D.: Cardinal characteristics and projective wellorders. Ann. Pure Appl. Logic 161(7), 916\u2013922 (2010)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"11","key":"385_CR15","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1016\/j.apal.2011.04.001","volume":"162","author":"V. Fischer","year":"2011","unstructured":"Fischer V., Friedman S.D., Zdomskyy L.: Projective wellorders and mad families with large continuum. Ann. Pure Appl. Logic 162(11), 853\u2013862 (2011)","journal-title":"Ann. Pure Appl. Logic"},{"key":"385_CR16","unstructured":"Friedman, S.D., Schrittesser, D.: Projective measure without projective Baire. Preprint, March (2013)"},{"key":"385_CR17","doi-asserted-by":"crossref","unstructured":"Geschke, S., Quickert, S.: On Sacks forcing and the Sacks property. In: Classical and New Paradigms of Computation and Their Complexity Hierarchies, vol. 23 of Trends Log. Stud. Log. Libr., pp. 95\u2013139. Kluwer, Dordrecht (2004)","DOI":"10.1007\/978-1-4020-2776-5_7"},{"issue":"2\u20133","key":"385_CR18","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/BF02808062","volume":"78","author":"M. Goldstern","year":"1992","unstructured":"Goldstern M., Judah H.: Iteration of Souslin forcing, projective measurability and the Borel conjecture. Isr. J. Math. 78(2\u20133), 335\u2013362 (1992)","journal-title":"Isr. J. Math."},{"key":"385_CR19","unstructured":"Goldstern, M.: Tools for your forcing construction. In: Set Theory of the Reals (Ramat Gan, 1991), vol. 6 of Israel Mathematical Conference Proceedings, pp. 305\u2013360. Bar-Ilan Univerity, Ramat Gan (1993)"},{"issue":"2","key":"385_CR20","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1002\/malq.200310016","volume":"49","author":"L. Halbeisen","year":"2003","unstructured":"Halbeisen L.: Making doughnuts of Cohen reals. Math. Logic Q. 49(2), 173\u2013178 (2003)","journal-title":"Math. Logic Q."},{"issue":"2","key":"385_CR21","first-page":"636","volume":"53","author":"J.I. Ihoda","year":"1988","unstructured":"Ihoda J.I.: $${\\Sigma_2^1}$$ \u03a3 2 1 -sets of reals. J. Symb. Logic 53(2), 636\u2013642 (1988)","journal-title":"J. Symb. Logic"},{"issue":"4","key":"385_CR22","doi-asserted-by":"crossref","first-page":"1188","DOI":"10.2307\/2274613","volume":"53","author":"J.I. Ihoda","year":"1988","unstructured":"Ihoda J.I., Shelah S.: Souslin forcing. J. Symb. Logic 53(4), 1188\u20131207 (1988)","journal-title":"J. Symb. Logic"},{"issue":"3","key":"385_CR23","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0168-0072(89)90016-X","volume":"42","author":"J.I. Ihoda","year":"1989","unstructured":"Ihoda J.I., Shelah S.: $${\\Delta^1_2}$$ \u0394 2 1 -sets of reals. Ann. Pure Appl. Logic 42(3), 207\u2013223 (1989)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"7","key":"385_CR24","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1016\/j.apal.2009.10.005","volume":"161","author":"D. Ikegami","year":"2010","unstructured":"Ikegami D.: Forcing absoluteness and regularity properties. Ann. Pure Appl. Logic 161(7), 879\u2013894 (2010)","journal-title":"Ann. Pure Appl. Logic"},{"key":"385_CR25","unstructured":"Jensen, R.B., Solovay, R.M.: Some applications of almost disjoint sets. In: Mathematical Logic and Foundations of Set Theory (Proceedings of International Colloquium, Jerusalem, 1968), pp. 84\u2013104. North-Holland, Amsterdam (1970)"},{"issue":"2","key":"385_CR26","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF01269952","volume":"32","author":"H. Judah","year":"1992","unstructured":"Judah H.: Exact equiconsistency results for $${\\varvec{\\Delta}^1_3}$$ \u0394 3 1 -sets of reals. Arch. Math. Logic 32(2), 101\u2013112 (1992)","journal-title":"Arch. Math. Logic"},{"key":"385_CR27","doi-asserted-by":"crossref","unstructured":"Judah, H.: Absoluteness for projective sets. In: Logic Colloquium \u201990 (Helsinki, 1990), vol. 2 of Lecture Notes Logic, pp. 145\u2013154. Springer, Berlin (1993)","DOI":"10.1017\/9781316718254.011"},{"key":"385_CR28","unstructured":"Judah, H.: $${\\Delta^1_3}$$ \u0394 3 1 -sets of reals. In: Set Theory of the Reals (Ramat Gan, 1991), vol. 6 of Israel Mathematical Conference Proceedings, pp. 361\u2013384. Bar-Ilan University, Ramat Gan, (1993)"},{"issue":"1","key":"385_CR29","doi-asserted-by":"crossref","first-page":"72","DOI":"10.2307\/2275325","volume":"58","author":"H. Judah","year":"1993","unstructured":"Judah H., Shelah S.: $${\\varvec{\\Delta}^1_3}$$ \u0394 3 1 -sets of reals. J. Symb. Logic 58(1), 72\u201380 (1993)","journal-title":"J. Symb. Logic"},{"issue":"5","key":"385_CR30","first-page":"301","volume":"34","author":"H. Judah","year":"1995","unstructured":"Judah H., Spinas O.: On the structure of $${\\varvec{\\Delta}^1_4}$$ \u0394 4 1 -sets of reals. Arch. Math. Logic 34(5), 301\u2013312 (1995)","journal-title":"Arch. Math. Logic"},{"issue":"2","key":"385_CR31","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s001530050059","volume":"36","author":"H. Judah","year":"1997","unstructured":"Judah H., Spinas O.: Large cardinals and projective sets. Arch. Math. Logic 36(2), 137\u2013155 (1997)","journal-title":"Arch. Math. Logic"},{"issue":"5(353)","key":"385_CR32","doi-asserted-by":"crossref","first-page":"3","DOI":"10.4213\/rm666","volume":"58","author":"V.G. Kanove\u012d","year":"2003","unstructured":"Kanove\u012d V.G., Lyubetski\u012d V.A.: On some classical problems in descriptive set theory. Uspekhi Mat. Nauk 58(5(353)), 3\u201388 (2003)","journal-title":"Uspekhi Mat. Nauk"},{"issue":"6","key":"385_CR33","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1007\/s00153-006-0008-0","volume":"45","author":"J. Kellner","year":"2006","unstructured":"Kellner J.: Preserving non-null with Suslin+ forcings. Arch. Math. Logic 45(6), 649\u2013664 (2006)","journal-title":"Arch. Math. Logic"},{"key":"385_CR34","unstructured":"Kellner, J.: Non elementary proper forcing. Preprint (2013)"},{"key":"385_CR35","unstructured":"Khomskii, Y.: Regularity properties and definability in the real number continuum. Ph.D. Thesis, University of Amsterdam (2012). ILLC Dissertations DS-2012-04"},{"key":"385_CR36","unstructured":"Laguzzi, G.: Arboreal forcing notions and regularity properties of the real line. Ph.D. Thesis, University of Vienna (2012)"},{"key":"385_CR37","unstructured":"Mathias, A.R.D.: A remark on rare filters. In: Infinite and Finite Sets (Colloquium, Keszthely, 1973; dedicated to P. Erd\u00f6s on his 60th birthday), vol. 3, pp. 1095\u20131097. Colloquium Mathematical Society, J\u00e1nos Bolyai, vol. 10. North-Holland, Amsterdam (1975)"},{"issue":"1","key":"385_CR38","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0003-4843(77)90006-7","volume":"12","author":"A.R.D. Mathias","year":"1977","unstructured":"Mathias A.R.D.: Happy families. Ann. Math. Logic 12(1), 59\u2013111 (1977)","journal-title":"Ann. Math. Logic"},{"issue":"1","key":"385_CR39","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1007\/BF02760523","volume":"48","author":"J. Raisonnier","year":"1984","unstructured":"Raisonnier J.: A mathematical proof of S. Shelah\u2019s theorem on the measure problem and related results. Isr. J. Math. 48(1), 48\u201356 (1984)","journal-title":"Isr. J. Math."},{"issue":"1","key":"385_CR40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02760522","volume":"48","author":"S. Shelah","year":"1984","unstructured":"Shelah S.: Can you take Solovay\u2019s inaccessible away?. Isr. J. Math. 48(1), 1\u201347 (1984)","journal-title":"Isr. J. Math."},{"issue":"2","key":"385_CR41","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1515\/JAA.2004.169","volume":"10","author":"S. Shelah","year":"2004","unstructured":"Shelah S.: Properness without elementaricity. J. Appl. Anal. 10(2), 169\u2013289 (2004)","journal-title":"J. Appl. Anal."},{"key":"385_CR42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1970696","volume":"92","author":"R.M. Solovay","year":"1970","unstructured":"Solovay R.M.: A model of set-theory in which every set of reals is Lebesgue measurable. Ann. Math. (2) 92, 1\u201356 (1970)","journal-title":"Ann. Math. (2)"},{"issue":"3","key":"385_CR43","doi-asserted-by":"crossref","first-page":"705","DOI":"10.2307\/2275753","volume":"60","author":"O. Spinas","year":"1995","unstructured":"Spinas O.: Generic trees. J. Symb. Logic 60(3), 705\u2013726 (1995)","journal-title":"J. Symb. Logic"},{"key":"385_CR44","doi-asserted-by":"crossref","first-page":"14","DOI":"10.4064\/fm-24-1-17-34","volume":"24","author":"E. Szpilrajn","year":"1935","unstructured":"Szpilrajn E.: Sur une classe de fonctions de M. Sierpiski et la classe correspondante d\u2019ensembles. Fund. Math. 24, 14\u201317 (1935)","journal-title":"Fund. Math."},{"key":"385_CR45","doi-asserted-by":"crossref","unstructured":"Truss, J.: Sets having calibre $${\\aleph _{1}}$$ \u2135 1 . In: Logic Colloquium 76 (Oxford, 1976), pp. 595\u2013612. Studies in Logic and Found. Math., vol. 87. North-Holland, Amsterdam (1977)","DOI":"10.1016\/S0049-237X(09)70447-1"},{"key":"385_CR46","doi-asserted-by":"crossref","unstructured":"Woodin, W.H.: On the consistency strength of projective uniformization. In: Proceedings of the Herbrand symposium (Marseilles, 1981), vol. 107 of Stud. Logic Found. Math., pp. 365\u2013384, Amsterdam, North-Holland (1982)","DOI":"10.1016\/S0049-237X(08)71895-0"},{"key":"385_CR47","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511542732","volume-title":"Forcing Idealized, volume 174 of Cambridge Tracts in Mathematics","author":"J. Zapletal","year":"2008","unstructured":"Zapletal J.: Forcing Idealized, volume 174 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge (2008)"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-014-0385-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-014-0385-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-014-0385-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,11]],"date-time":"2019-08-11T06:16:53Z","timestamp":1565504213000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-014-0385-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,3]]},"references-count":47,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["385"],"URL":"https:\/\/doi.org\/10.1007\/s00153-014-0385-8","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,3]]}}}