{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T07:08:56Z","timestamp":1749020936372},"reference-count":5,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T00:00:00Z","timestamp":1684368000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T00:00:00Z","timestamp":1684368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the book Cardinal Invariants on Boolean Algebras by J. Donald Monk many such cardinal functions are defined and studied. Among them several are generalizations of well known cardinal characteristics of the continuum. Alongside a long list of open problems is given. Focusing on half a dozen of those cardinal invariants some of those problems are given an answer here, which in most of the cases is a definitive one. Most of them can be divided in two groups. The problems of the first group ask about the change on those cardinal functions when going from a given infinite Boolean algebra to its simple extensions, while in the second group the comparison is between a couple of given infinite Boolean algebras and their free product.<\/jats:p>","DOI":"10.1007\/s00153-023-00872-8","type":"journal-article","created":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T11:03:03Z","timestamp":1684407783000},"page":"947-963","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Questions on cardinal invariants of Boolean algebras"],"prefix":"10.1007","volume":"62","author":[{"given":"Mario Jard\u00f3n","family":"Santos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,18]]},"reference":[{"issue":"1","key":"872_CR1","doi-asserted-by":"publisher","first-page":"94","DOI":"10.2307\/2273792","volume":"50","author":"JE Baumgartner","year":"1985","unstructured":"Baumgartner, J.E., Dordal, P.: Adjoining dominating functions. J. Symbol. Logic 50(1), 94\u2013101 (1985)","journal-title":"J. Symbol. Logic"},{"key":"872_CR2","series-title":"2, 3","doi-asserted-by":"publisher","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, Matthew, Kanamori, Akihiro (eds.) Handbook of Set Theory. 2, 3, vol. 1, pp. 395\u2013489. Springer, Dordrecht (2010)"},{"key":"872_CR3","unstructured":"Brendle, J.: Forcing and the structure of the real line: the Bogot\u00e1 lectures. Lecture notes (2009)"},{"key":"872_CR4","unstructured":"Koppelberg, S.: Handbook of Boolean Algebras. North Holland (1989)"},{"key":"872_CR5","doi-asserted-by":"crossref","unstructured":"Monk, J.D.: Cardinal Invariants on Boolean Algebras, 2nd edn. Birkhauser (2014)","DOI":"10.1007\/978-3-0348-0730-2"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-023-00872-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-023-00872-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-023-00872-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,20]],"date-time":"2023-09-20T03:27:43Z","timestamp":1695180463000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-023-00872-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,18]]},"references-count":5,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["872"],"URL":"https:\/\/doi.org\/10.1007\/s00153-023-00872-8","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,18]]},"assertion":[{"value":"18 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The author declares that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}