Ordinal notations based on a hierarchy of inaccessible cardinals
type: Item
instance of: scholarly article
title: Ordinal notations based on a hierarchy of inaccessible cardinals
zbMATH Open document ID: 0656.03038
DOI: 10.1016/0168-0072(87)90079-0
author: Wolfram Pohlers
published in: Annals of Pure and Applied Logic
publication date: 1987-01-01T00:00:00Z
review text: The author generalizes results on notation systems of \textit{K. Schütte} [Proof theory (1977; Zbl 0367.02012)] and \textit{W. Buchholz} [Lect. Notes Math. 500, 4-25 (1975; Zbl 0342.02021)], and obtains, via so-called Skolem hulls and 2-place functions from the ordinals into the inaccessible cardinals, a new ordinal notation system. This research was motivated by the fact that \((\Delta^ 1_ 2-CA)+BI\) has a model at the first recursively inaccessible ordinal in the constructible hierarchy.
Mathematics Subject Classification ID: 03F15
zbMATH DE Number: 4070890
zbMATH Keywords: Skolem hulls
zbMATH Keywords: inaccessible cardinals
zbMATH Keywords: ordinal notation system
zbMATH Keywords: recursively inaccessible ordinal
zbMATH Keywords: constructible hierarchy
MaRDI profile type: Publication
full work available at URL: 0168-0072(87)90079-0
OpenAlex ID: W2046420469
cites work: A simplification of the Bachmann method for generating large countable ordinals
cites work: Q4109654
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cites work: A well-ordering proof for Feferman's theoryT 0
cites work: Q3041187
cites work: ϱ-inaccessible ordinals, collapsing functions and a recursive notation system
cites work: Q4143279
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description: scientific article; zbMATH DE number 4070890