Finite \(H\)-dimension does not imply expressive completeness
type: Item
instance of: scholarly article
title: Finite \(H\)-dimension does not imply expressive completeness
zbMATH Open document ID: 0811.03027
DOI: 10.1007/BF01049409
published in: Journal of Philosophical Logic
publication date: 1994-11-09T00:00:00Z
review text: The monadic first-order language (formulas in this language are called monadic) is obtained from a given first-order language by adding a set of monadic predicates. A monadic first-order formula with a single free variable is called connective. A class of first-order structures \(K\) has \(H\)-dimension \(d\) if \(d\) is the least number such that every monadic formula is \(K\)-equivalent to a monadic formula using at most \(d\) bound variables. It is known that if a class of structures has a finite basis of connectives, then it has finite \(H\)-dimension. In this paper the other direction (a conjecture of D. Gabbay) is refuted.
reviewed by: L.A.Chagrova
Mathematics Subject Classification ID: 03C07
zbMATH DE Number: 683099
zbMATH Keywords: expressive completeness
zbMATH Keywords: monadic first-order language
zbMATH Keywords: monadic predicates
zbMATH Keywords: first-order structures
zbMATH Keywords: \(H\)-dimension
author: Ian Hodkinson
MaRDI profile type: Publication
cites work: Separation in nonlinear time models
cites work: Preservation of expressive completeness in temporal models
cites work: The logic of time. A model-theoretic investigation into the varieties of temporal ontology and temporal discourse.
cites work: Model theory.
cites work: Q4281254
cites work: Q3835817
cites work: The \(k\)-variable property is stronger than H-dimension \(k\)
cites work: Definability with bounded number of bound variables
cites work: Q3246315
cites work: Q5556395
cites work: Axiomatisation and decidability of \(F\) and \(P\) in cyclical time
cites work: Expressive completeness of temporal logic of trees
cites work: Expressiveness and completeness of an interval tense logic
description: scientific article; zbMATH DE number 683099