{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T17:14:30Z","timestamp":1774458870946,"version":"3.50.1"},"reference-count":31,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2018,12,17]],"date-time":"2018-12-17T00:00:00Z","timestamp":1545004800000},"content-version":"vor","delay-in-days":16,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study a transfinite iteration of the ordinal Hessenberg natural sum obtained by taking suprema at limit stages. We show that such an iterated natural sum differs from the more usual transfinite ordinal sum only for a finite number of iteration steps. The iterated natural sum of a sequence of ordinals can be obtained as a mixed sum (in an order\u2010theoretical sense) of the ordinals in the sequence; in fact, it is the largest mixed sum which satisfies a finiteness condition. We introduce other infinite natural sums which are invariant under permutations and show that all the sums under consideration coincide in the countable case.<\/jats:p>","DOI":"10.1002\/malq.201600092","type":"journal-article","created":{"date-parts":[[2018,12,17]],"date-time":"2018-12-17T15:20:42Z","timestamp":1545060042000},"page":"514-528","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Some transfinite natural sums"],"prefix":"10.1002","volume":"64","author":[{"given":"Paolo","family":"Lipparini","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica Universit\u00e0 di Roma \u201cTor Vergata\u201d Viale della Ricerca Scientifica 00133 Rome Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,12,17]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201600006"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066783"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-7.3.429"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-88514-3"},{"key":"e_1_2_8_6_1","first-page":"0110641","article-title":"Review of [17]","author":"Bagemihl F.","year":"1961","journal-title":"Math. 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