How to develop Proof‐Theoretic Ordinal Functions on the basis of admissible ordinals
作者:
Michael Rathjen,
期刊:
Mathematical Logic Quarterly
(WILEY Available online 1993)
卷期:
Volume 39,
issue 1
页码: 47-54
ISSN:0942-5616
年代: 1993
DOI:10.1002/malq.19930390107
出版商: WILEY‐VCH Verlag Berlin GmbH
关键词: Proof theory;Ordinal representation system;Collapsing function;Admissible ordinal
数据来源: WILEY
摘要:
AbstractIn ordinal analysis of impredicative theories so‐called collapsing functions are of central importance. Unfortunately, the definition procedure of these functions makes essential use of uncountable cardinals whereas the notation system that they call into being corresponds to a recursive ordinal. It has long been claimed that, instead, one should manage to develop such functions directly on the basis of admissible ordinals. This paper is meant to show how this can be done. Interpreting the collapsing functions as operating directly on admissible sets also renders a new and perspicuous approach to well‐ordering proofs possible. MSC: 03F15, 03
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