An independence result for \((\Pi^ 1_ 1-CA)+BI\)
type: Item
instance of: scholarly article
title: An independence result for \((\Pi^ 1_ 1-CA)+BI\)
zbMATH Open document ID: 0636.03052
DOI: 10.1016/0168-0072(87)90078-9
author: Wilfried Buchholz
published in: Annals of Pure and Applied Logic
publication date: 1987-01-01T00:00:00Z
full work available at URL: buchholz wilfried 3842.pdf
review text: This paper meets a combinatorial problem by modern means of proof theory, which can be clothed in the legend of Hercules and the Hydra: A hydr AB This paper meets a combinatorial problem by modern means of proof theory, which can be clothed in the legend of Hercules and the Hydra: A hydra is a finite tree, each node of which is labelled by some element of the set \(\{+\} \cup (\omega + 1)\). Cutting a head ( = leaf of the tree) of the hydra is defined in such a way that from stroke to stroke the beast seems to increase. But surprisingly, it can be proven.
Mathematics Subject Classification ID: 03F20
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 03F05
zbMATH DE Number: 4035824
zbMATH Keywords: proof theory
zbMATH Keywords: Hercules
zbMATH Keywords: Hydra
zbMATH Keywords: finite tree
zbMATH Keywords: wellfounded trees
MaRDI profile type: Publication
OpenAlex ID: W2084179139
cites work: Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
cites work: A Short Proof of Two Recently Discovered Independence Results Using Recursion Theoretic Methods
cites work: Rapidly growing Ramsey functions
cites work: Accessible Independence Results for Peano Arithmetic
cites work: Built-up systems of fundamental sequences and hierarchies of number-theoretic functions
cites work: Q5605873
description: scientific article; zbMATH DE number 4035824