{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T13:53:44Z","timestamp":1769522024979,"version":"3.49.0"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"Austrian Science Foundation","award":["Y1012-N35"],"award-info":[{"award-number":["Y1012-N35"]}]},{"name":"CONACyT","award":["A1-S-16164"],"award-info":[{"award-number":["A1-S-16164"]}]},{"name":"PAPIIT","award":["IN104220"],"award-info":[{"award-number":["IN104220"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> A question dating to Marde\u0161i\u0107 and Prasolov\u2019s 1988 work [S.\u00a0Marde\u0161i\u0107 and A.\u00a0V. Prasolov, Strong homology is not additive, Trans. Amer. Math. Soc.\u00a0307(2) (1988) 725\u2013744], and motivating a considerable amount of set theoretic work in the years since, is that of whether it is consistent with the ZFC axioms for the higher derived limits [Formula: see text]\u00a0[Formula: see text] of a certain inverse system [Formula: see text] indexed by [Formula: see text] to simultaneously vanish. An equivalent formulation of this question is that of whether it is consistent for all [Formula: see text]-coherent families of functions indexed by [Formula: see text] to be trivial. In this paper, we prove that, in any forcing extension given by adjoining [Formula: see text]-many Cohen reals, [Formula: see text] vanishes for all [Formula: see text]. Our proof involves a detailed combinatorial analysis of the forcing extension and repeated applications of higher-dimensional [Formula: see text]-system lemmas. This work removes all large cardinal hypotheses from the main result of [J. Bergfalk and C. Lambie-Hanson, Simultaneously vanishing higher derived limits, Forum Math. Pi\u00a09 (2021) e4] and substantially reduces the least value of the continuum known to be compatible with the simultaneous vanishing of [Formula: see text] for all [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219061322500192","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T09:18:28Z","timestamp":1655457508000},"source":"Crossref","is-referenced-by-count":8,"title":["Simultaneously vanishing higher derived limits without large cardinals"],"prefix":"10.1142","volume":"23","author":[{"given":"Jeffrey","family":"Bergfalk","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik, Kurt G\u00f6del Research Center, Universit\u00e4t Wien, Kolingasse 14-16, 1010 Wien, Austria"}]},{"given":"Michael","family":"Hru\u0161\u00e1k","sequence":"additional","affiliation":[{"name":"Centro de Ciencas Matem\u00e1ticas, Universidad Nacional Aut\u00f3noma de M\u00e9xico (UNAM ), A.P. 61-3, Xangari, Morelia, Michoac\u00e1n 58089, Mexico"}]},{"given":"Chris","family":"Lambie-Hanson","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Czech Academy of Sciences, \u017ditn\u00e1 25, 110 00 Praha 1, Czechia"}]}],"member":"219","published-online":{"date-parts":[[2022,12,17]]},"reference":[{"key":"S0219061322500192BIB002","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0098398","volume-title":"Topics in Set Theory: Lebesgue Measurability, Large Cardinals, Forcing Axioms, Rho-Functions","volume":"1476","author":"Bekkali M.","year":"1991"},{"issue":"1","key":"S0219061322500192BIB003","doi-asserted-by":"crossref","first-page":"71","DOI":"10.4064\/fm140-4-2016","volume":"236","author":"Bergfalk J.","year":"2017","journal-title":"Fund. 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