Pell equations and exponentiation in fragments of arithmetic
type: Item
instance of: scholarly article
title: Pell equations and exponentiation in fragments of arithmetic
zbMATH Open document ID: 0855.03034
DOI: 10.1016/0168-0072(95)00018-6
author: Paola D'Aquino
published in: Annals of Pure and Applied Logic
publication date: 1996-07-23T00:00:00Z
review text: The paper is devoted to the study of the relative strength of two axioms: (1) every Pell equation has a nontrivial solution, and (2) exponentiation is total. It is shown that they are equivalent over \(\text{IE}_1\). Further the graph of the exponential function is defined using only existentially bounded quantifiers in the language of arithmetic expanded with the symbol \#, where \(\# (x, y)= x^{[\log_2 y]}\). The recursion laws of exponentiation are proved in the corresponding fragement.
reviewed by: Roman Murawski
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 908453
zbMATH Keywords: relative strength of two axioms
zbMATH Keywords: Pell equation
zbMATH Keywords: exponentiation
zbMATH Keywords: recursion laws
MaRDI profile type: Publication
full work available at URL: 0168-0072(95)00018-6
OpenAlex ID: W2059666897
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description: scientific article; zbMATH DE number 908453