Mathematical proof theory in the light of ordinal analysis
type: Item
instance of: scholarly article
title: Mathematical proof theory in the light of ordinal analysis
zbMATH Open document ID: 1041.03041
DOI: 10.1023/A:1020892011851
author: Reinhard Kahle
published in: Synthese
publication date: 2003-04-27T00:00:00Z
review text: The author presents a non-technical, introductory account of the present state of proof theory, centered about ordinal analysis. It gives a very good view of the ``landscape'', to beginners and outsiders, with an extensive bilbiography and guide to it. \textit{W. Pohler}'s article in Handbook of proof theory [Amsterdam: Elsevier. Stud. Logic. Found. Math. 137, 209--335 (1998; Zbl 0940.03066)] treats about the same area with much more advanced technology and details. And so, these two articles complement each other. The author talks about subsystems of analysis, admissible set theory, explicit mathematics, theories of inductive definitions, constructive set theory, and Martin-Löf's type theory. He provides ``A snapshot of the landscape'': a table of these theories and their proof-theoretic ordinals.
Mathematics Subject Classification ID: 03F15
Mathematics Subject Classification ID: 03F35
zbMATH DE Number: 1901269
zbMATH Keywords: ordinal analysis
zbMATH Keywords: survey
zbMATH Keywords: proof theory
MaRDI profile type: Publication
full work available at URL: a:1020892011851
OpenAlex ID: W2047781465
description: scientific article; zbMATH DE number 1901269