A class of \(\Sigma_{3}^{0}\) modular lattices embeddable as principal filters in \({\mathcal L}^*(V_\infty)\)
type: Item
instance of: scholarly article
title: A class of \(\Sigma_{3}^{0}\) modular lattices embeddable as principal filters in \({\mathcal L}^*(V_\infty)\)
zbMATH Open document ID: 1173.03032
published in: Archive for Mathematical Logic
publication date: 2008-10-16T00:00:00Z
review text: Let \(V_\infty\) be an effective infinite-dimensional vector space over a computable field, and \({\mathcal L}^*(V_\infty)\) be the lattice of c.e. subspaces of \(V_\infty\) modulo the equivalence relation \(=^*\) (where \(A =^* B\) if the sets \(A\) and \(B\) differ by finitely many elements). The paper establishes certain structural properties of \({\mathcal L}^*(V_\infty)\), which, combined with an earlier result of the author [``Quasimaximality and principal filters isomorphism between \({\mathcal E}^*\) and \({\mathcal L}^*(V_\infty)\)'', Arch. Math. Logic 43, No. 3, 415--424 (2004; Zbl 1059.03040)], lead to a characterization of the principal filters of \({\mathcal L}^*(V_\infty)\).
reviewed by: Marius Zimand
Mathematics Subject Classification ID: 03C57
Mathematics Subject Classification ID: 03D25
Mathematics Subject Classification ID: 06C05
zbMATH DE Number: 5351802
zbMATH Keywords: computable vector space
zbMATH Keywords: filters of quasimaximal spaces
zbMATH Keywords: lattice product
author: R. D. Dimitrov
MaRDI profile type: Publication
full work available at URL: s00153-008-0078-2
OpenAlex ID: W2076597235
cites work: Quasimaximality and principal filters isomorphism between \({\mathcal E}^*\) and \({\mathcal L}^*(V_\infty)\)
cites work: Undecidability of \(L(F_{\infty})\) and other lattices of r.e. substructures
cites work: Q4249725
cites work: Q5639727
cites work: Recursively enumerable vector spaces
cites work: Q5573961
cites work: Q4040892
DOI: 10.1007/S00153-008-0078-2
description: scientific article; zbMATH DE number 5351802