Format:
Online-Ressource
ISSN:
1521-3870
Content:
Abstract: G. Jäger gave in Arch. Math. Logik Grundlagenforsch. 24 (1984), 49‐62, a recursive notation system on a basis of a hierarchy Iαß of α‐inaccessible regular ordinals using collapsing functions following W. Buchholz in Ann. Pure Appl. Logic 32 (1986), 195‐207. Jäger's system stops, when ordinals α with Iα0 = α enter. This border is now overcome by introducing additional a hierarchy Jαß of weakly inaccessible Mahlo numbers, which is defined similarly to the Jäger hierarchy. An ordinal μ is called Mahlo, if every normal‐function f: μ → μ has regular fixpoints. Collapsing is defined for both Mahlo and simply regular ordinals such that for every Mahlo ordinal μ out of the J‐hierarchy Ψμα is a regular σ such that Iσ0 = σ. For these regular σ again collapsing functions Ψσ are defined. To get a proper systematical order into the collapsing procedure, a pair of ordinals is associated to σ and α, and the definition of Ψσα is given by recursion on a suitable well‐ordering of these pairs. Thus a fairly large system of ordinal notations can be established. It seems rather straightforward, how to extend this setting further.
In:
volume:38
In:
number:1
In:
year:2006
In:
pages:431-456
In:
extent:26
In:
Mathematical logic quarterly, Berlin : Wiley-VCH, 1955-, 38, Heft 1 (2006), 431-456 (gesamt 26), 1521-3870
Language:
English
DOI:
10.1002/malq.19920380142
URN:
urn:nbn:de:101:1-2024012904015866374790
URL:
https://doi.org/10.1002/malq.19920380142
URL:
https://nbn-resolving.org/urn:nbn:de:101:1-2024012904015866374790
URL:
https://d-nb.info/1317457188/34
URL:
https://doi.org/10.1002/malq.19920380142