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In particular, Shelah's Strong Hypothesis is shown to be equivalent to the assertion that for any singular cardinal \u03c3 of cofinality \u03c9, there is a size collection<jats:italic>Q<\/jats:italic>of countable subsets of \u03c3 with the property that for any infinite subset<jats:italic>a<\/jats:italic>of \u03c3, there is a member of<jats:italic>Q<\/jats:italic>meeting<jats:italic>a<\/jats:italic>in an infinite\u00a0set.<\/jats:p>","DOI":"10.1002\/malq.201900039","type":"journal-article","created":{"date-parts":[[2021,5,29]],"date-time":"2021-05-29T13:44:06Z","timestamp":1622295846000},"page":"59-76","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Meeting numbers and pseudopowers"],"prefix":"10.1002","volume":"67","author":[{"given":"Pierre","family":"Matet","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Caen \u2013 CNRS Laboratoire de Math\u00e9matiques BP 5186, 14032 Caen Cedex France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,5,29]]},"reference":[{"key":"e_1_2_13_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90057-9"},{"key":"e_1_2_13_3_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm212-3-4"},{"key":"e_1_2_13_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-018-0789-8"},{"key":"e_1_2_13_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2011-05355-9"},{"key":"e_1_2_13_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0346-0330-0"},{"key":"e_1_2_13_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2016.08.016"},{"key":"e_1_2_13_8_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm205-1-3"},{"key":"e_1_2_13_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201200008"},{"key":"e_1_2_13_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2015.05.001"},{"key":"e_1_2_13_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201600047"},{"key":"e_1_2_13_12_1","unstructured":"P.Matet Versions forP\u03ba(\u03bb)of two results of Shelah on Diamond \u2013 Part 1 preprint."},{"key":"e_1_2_13_13_1","unstructured":"P.Matet Applications of pcf theory to the study of ideals onP\u03ba(\u03bb) preprint."},{"key":"e_1_2_13_14_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-03-03202-1"},{"key":"e_1_2_13_15_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-08-09411-2"},{"key":"e_1_2_13_16_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1278682214"},{"key":"e_1_2_13_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02787123"},{"key":"e_1_2_13_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02807866"},{"key":"e_1_2_13_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-2080-7_25"},{"key":"e_1_2_13_20_1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537854.001.0001","volume-title":"Cardinal Arithmetic, Oxford Logic Guides","author":"Shelah S.","year":"1994"},{"key":"e_1_2_13_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761035"},{"key":"e_1_2_13_22_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4064\/fm-166-1-2-1-82","article-title":"On what I do not understand (and have something to say): Part I","volume":"166","author":"Shelah S.","year":"2000","journal-title":"Fund. 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