The order on the rationals has an orthogonal order with the same order type
type: Item
instance of: scholarly article
title: The order on the rationals has an orthogonal order with the same order type
zbMATH Open document ID: 1238.06002
author: Imed Zaguia
author: Norbert Sauer
published in: Order
publication date: 2011-12-13T00:00:00Z
review text: The authors study the existence of linear orders orthogonal to the order of the rationals and prove the theorem that if \(\nu \geqslant {\omega ^2}\) is a countable ordinal then the order of the rationals \(\eta = \left( {{\mathbb Q}, \leqslant } \right)\) has an orthogonal linear order of order-type \(\nu \) and \(\eta \) has an orthogonal linear order of order-type \(\eta \). \(\omega \) denotes the first infinite countable ordinal, \(\mathbb{Q}\) denotes the set of rational numbers.
Mathematics Subject Classification ID: 06A05
zbMATH DE Number: 5988083
zbMATH Keywords: ordered set
zbMATH Keywords: autonomous set
zbMATH Keywords: order-preserving map
zbMATH Keywords: endomorphism
zbMATH Keywords: clone
zbMATH Keywords: perpendicular orders
zbMATH Keywords: orthogonal orders
zbMATH Keywords: ordered relational structures
MaRDI profile type: Publication
full work available at URL: s11083-010-9176-y
OpenAlex ID: W2027053128
cites work: Relational systems with trivial endomorphisms and polymorphisms
cites work: The number of orthogonal permutations
cites work: Unary polynomials in algebras. I
cites work: Weak orders admitting a perpendicular linear order
DOI: 10.1007/S11083-010-9176-Y
description: scientific article; zbMATH DE number 5988083