Iterated trees and fragments of arithmetic
type: Item
instance of: scholarly article
title: Iterated trees and fragments of arithmetic
zbMATH Open document ID: 0826.03028
DOI: 10.1007/BF01270390
author: Yue Yang
published in: Archive for Mathematical Logic
publication date: 1995-11-28T00:00:00Z
review text: The paper is devoted to some problems connected with the so-called Recursion Theory in Fragments of Arithmetic. It is an analogue of reverse mathematics. The main result of the paper states that the general \(O^{(n)}\)-priority method succeeds iff the induction scheme for \(\Sigma_n\) formulas \((I \Sigma_n)\) holds. As a consequence one gets that if we have an iterated trees style \(O^{(n)}\)-priority proof of a theorem, then we know that the theorem can be proved in the fragment \(\text{PA}^- + I \Sigma_n\). It is also shown that the iterated trees framework is in fact applicable to the finite injury level.
reviewed by: Roman Murawski
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 761853
zbMATH Keywords: Recursion Theory in Fragments of Arithmetic
zbMATH Keywords: reverse mathematics
zbMATH Keywords: \(O^{(n)}\)-priority method
zbMATH Keywords: iterated trees
zbMATH Keywords: finite injury
MaRDI profile type: Publication
cites work: Countable algebra and set existence axioms
cites work: Topological Framework for Non‐Priority
cites work: Q3884109
cites work: On some games which are relevant to the theory of recursively enumerable sets
cites work: Q3480023
cites work: Finite injury and Σ1-induction
full work available at URL: https://doi.org/10.1007/bf01270390
OpenAlex ID: W2073662919
description: scientific article; zbMATH DE number 761853