{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T08:43:46Z","timestamp":1695890626294},"reference-count":7,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5430,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>G. J\u00e4ger gave in Arch. Math. Logik Grundlagenforsch. 24 (1984), 49\u201062, a recursive notation system on a basis of a hierarchy I\u03b1\u00df of \u03b1\u2010inaccessible regular ordinals using collapsing functions following W. Buchholz in Ann. Pure Appl. Logic 32 (1986), 195\u2010207. J\u00e4ger's system stops, when ordinals \u03b1 with I\u03b10 = \u03b1 enter. This border is now overcome by introducing additional a hierarchy J\u03b1\u00df of weakly inaccessible Mahlo numbers, which is defined similarly to the J\u00e4ger hierarchy. An ordinal \u03bc is called Mahlo, if every normal\u2010function <jats:italic>f<\/jats:italic> : \u03bc \u2192 \u03bc has regular fixpoints. Collapsing is defined for both Mahlo and simply regular ordinals such that for every Mahlo ordinal \u03bc out of the J\u2010hierarchy \u03a8\u03bc\u03b1 is a regular \u03c3 such that I\u03c30 = \u03c3. For these regular \u03c3 again collapsing functions \u03a8\u03c3 are defined. To get a proper systematical order into the collapsing procedure, a pair of ordinals is associated to \u03c3 and \u03b1, and the definition of \u03a8\u03c3\u03b1 is given by recursion on a suitable well\u2010ordering of these pairs. Thus a fairly large system of ordinal notations can be established. It seems rather straightforward, how to extend this setting further.<\/jats:p>","DOI":"10.1002\/malq.19920380142","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T05:49:03Z","timestamp":1180417743000},"page":"431-456","source":"Crossref","is-referenced-by-count":0,"title":["A NOTATION SYSTEM FOR ORDINAL USING \u03a8\u2010FUNCTIONS ON INACCESSIBLE MAHLO NUMBERS"],"prefix":"10.1002","volume":"38","author":[{"given":"Helmut","family":"Pfeiffer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Pfeiffer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(86)90052-7"},{"key":"e_1_2_1_3_2","volume-title":"Set Theory: An Introduction to Large Cardinals","author":"Drake F. R.","year":"1974"},{"key":"e_1_2_1_4_2","unstructured":"Ehring Th. Ein primitiv rekursives Bezeichnungssystem \u00fcber einer Hierarchie von Mahlofunktionen. Dissertation Hannover1990."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02007140"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01651328"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02017490"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01625837"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380142","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380142","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:34:18Z","timestamp":1695846858000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380142"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380142"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380142","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}